While some games can be nothing but sprite graphics or Polygonal Graphics, some games mix them up.
This is usually for technical reasons. Polygon graphics had been around for years, but it wasn't until the 90s that extensive polygon graphics would be practical and affordable for mass market games, but just barely. Polygon count, texture resolution, shading, mapping, etc. were very limited at the time, at least for systems people could actually afford.
It was possible to make everything out of polygons (save for things like the HUD), but only with certain types of games, and they still had to make some sacrifices (like an extremely limited color depth in the textures). This trope is about games that relied on a combination of sprites and polygon models to get the most details in one scene.
This is usually in the form of fully 3-D areas, with heavily scaling and rotating sprites as characters and/or objects (a technique called "billboarding"), or full-screen bitmaps used as the backgrounds with polygon models in the foreground.
Earlier games with 3D environments containing sprites had very obvious limitations; single-sided sprites in a 3D arena, for example, will appear to rotate to face the player as they move around. One solution to create a pseudo-3D sprite object with a high level of detail is to use two sprites, arranged at right angles. This looks moderately okay from every angle, but not very good from any; this is particularly true if it can be viewed from above, where it will look like a letter x made of single-pixel lines. This is sometimes still used for grass and other insubstantial-yet-complex plant life that will need to be repeated extensively, especially if it needs to be semi-transparent. Another method is to map a partially transparent texture to the outside of a sphere or cylinder; this allows the object to be viewed from all sides without requiring it to be modelled in detail.
Systems from the Sega Dreamcast onward (with the exception of the DS, which is in the same class as the fifth generation) have largely dropped this, due to the huge polygon counts allowing full 3-D models of even the smallest objects, and have the texture resolution to show the detail of those objects. Some extremely complex effects such as smoke, explosions and fire are normally still rendered as two-dimensional objects; this is hardly surprising, as even big-budget CGI movies tend to use practical effects rather than attempt to simulate these. This trope does continue in spirit in even the latest games, with 2D effects being used in place of more complex geometry; bump and normal mapping both operate by using a 2D image to add detail to a 3D object without using additional polygons.
It should be noted that the horizon and the sky in even recent games are usually pre-rendered and then drawn onto the interior of a cylinder, sphere, or hemisphere, since it would be an unnecessary waste of processing power to create such distant objects as level geometry. Effects such as snow and rain are usually also achieved this way, by creating a series of concentric cylinders with an animated rain effect mapped to them, which are centred on the player's position.
Can overlap with Video Game 3D Leap, Digitized Sprites.
Most pre-QuakeFPSs have an appearance consistant with this trope, but technically do not qualify since their environments do not use polygon meshes (as defined today) to create walls. They use various methods to create pseudo-3D backgrounds, with enemies, powerups and decorations being scaled sprites. Doom, for example, uses a texture fill method similar to 3D extrude functions to give an otherwise flat map an illusion of height, though the engine has no meaningful Z (vertical) axis and does not use polygon meshes. Some later examples use voxels (I.E.: Buildenginegames) or polygons (I.E.: Dark Forces) for some objects as well.
2D foregrounds, 3D backgrounds:
Most early flight sims use a combination of polygon objects and sprite effects; cockpit displays are completely 2D, and effects like smoke and explosions the same. Examples include F-29 Retaliator and Gunship 2000.
Descent is the ancestor of true 3D shooters, and is notable in that, while its enemies and levels are rendered in 3D with polygons, all powerups and items, as well as some weapon effects, are rendered with sprites.
Quake is the first traditional First-Person Shooter to be in full 3D, and showcases many concepts that are impossible in the pseudo-3D engines that went before; rooms above rooms, spiral staircases, enemies leaping, swimming and so on. It still mixes in sprites for some explosive effects, which are always scaled and facing the camera. This is replicated in only some later games, although Unreal uses both a polygon and a sprite-style explosion in the expansion pack. Unusually, some of these earlier games have 3D fire effects in torches and similar; as the general level of detail in games climbed, however, it became clear that equally convincing 3D fire would not be feasible.
Well, not completely impossible. Marathon has a pseudo-3D engine, but is capable of having rooms above rooms, or even rooms that are distinct, yet occupy the same "space" as each other.
Duke Nukem 3D has this kind of alien geometry as well, only in several levels the developers went all out and uses it on purpose to create 720 degree circles and similar stunts.
Note that these are tricks. The engine never really has rooms above other rooms; things like invisible teleporters and unseen horizontal space changes are used to give the rooms-above-rooms illusion.
Rise of the Triad is in fact the first game to have not just room-over-room but level over level within a room, allowing for full multi-level firefights and actions.
An interesting variation: the Nintendo 64 version of Duke Nukem 3D features some things, such as explosion effects, being rendered in polygons while the enemies and weapons are all still sprites. These new polygon effects are not present in the original PC version of the game.
Star Fox. Yes, the SNES one, and it is probably the earliest console example: the much-touted Super FX chip built into its cartridge is basically the first console 3D accelerator. Low poly count, but polys nonetheless. Explosions, ejected reptilian pilots, and asteroids are all sprites overlaid with Mode 7.
In Super Mario 64, trees are billboarded sprites, while most other parts of the environment are polygons.
The coins are billboarded sprites too, although this is camouflaged—a 2D animation of a spinning coin is used to create the illusion of the coins being 3D objects.
Anything spherical is a sprite: Bob-Ombs, those cannonballs that roll around in the first main level, and the water spiders.
Mario 64 also features an inversion of this trope, where a 3D effect is used to create a 2D effect. This is the mirror room; rather than use light sourcing and surface properties to create a mirrored surface, the room itself is mirrored and bisected by a transparent wall where the mirror is supposed to be. A second Mario is placed in the other side of the room and mirrors the player's control input. This is actually a commonly used trick in games even today; it allows realistic reflections without resorting to framebuffer effects (which are limited by the internal render resolution and look pixellated up close), non-dynamic reflection mapping, or hardware-intensive real-time raytracing. However, it only works with flat mirrors.
Taken to an extreme in the DS re-release, where the player can grab a Power Flower in the room while controlling Luigi, allowing him to go through the mirror. This is required to get to Chief Chilly Challenge and unlock Wario.
Turok 2 features an interesting graphical glitch that shows how the sprites are scaled; the game measures the distance from player object to sprite to figure out how large the sprite should be on-screen. Unfortunately, it has no way to compensate for the sniper zoom, meaning a 2D effect will appear to shrink as you zoom in and grow as you zoom out.
Also from the Mega Man franchise, Mega Man: Maverick Hunter X. 3D renders of everything about the SNES original...except the spikes (they're even pixillated!). Elements of the backgrounds (e.g. the jets in Storm Eagle's stage) are obviously 2D as well, so this example could fit in any of the other sections of this trope. Course, it is an action game on PSP, which only has so much memory to spend on moving/exploding objects...
Mario Kart 64 - Practically everything that isn't background is 2-D, including the playable characters and their karts.
Klonoa: Door to Phantomile uses sprites on 3D environments; it then procedes to make the most of this, having enemies and obstacles in the foreground and background, or paths that bent around in all sorts of directions, even looping around in some instances.
Xenogears: Has aged particularly poorly, due to the low quality of sprites rendering them messy blobs of pixels even at normal camera angles, though the 3D elements have held up better than other contemporary examples.
Paper Mario series, whose very title lampshades it. It's in full effect in the first game and Sticker Star, but in The Thousand-Year Door and Super the only things that are really 2D are the items and skyboxes. The characters and some scenery are just 2D sprites on flat polygon frameworks, like the Game and Watch example further down.
If you're emulating the game, with certain settings, you REALLY notice the difference between the "duller" sprites and the "sharper" 3D effects. Which, ironically, in some cases makes the effects look even more awesome. But note that they simply took the sprite graphics and put them on polygons in some cases, causing the "dull" images themselves to become "sharp".
The original Tales of Destiny overworld engine, used by Destiny and the Phantasia remake. Uses the in-town sprites laid on a 3-D globe.
The WarGames RTS game has buildings, vehicles and mechs in full 3D, but all infantry units are sprites, presumably because making detailed 3D models of suitable size would have been a waste of resources. It results in many players not using infantry at all simply because using mechanized units is so much more pleasing to the eye. See this screenshot.
Ragnarok Online uses cartoony sprites for all characters and enemies, in 3D environments.
Umihara Kawase Shun uses polygonal platforms but everything else, the rest of the background included, is sprites.
Mischief Makers uses sprite objects, but polygonal levels. To make things more confusing, the sprites are clearly based off of 3D models. The effect is... interesting. The game is awesome, anyway.
Tomb Raider 1 and 2 use sprites extensively for pickup objects and small plants and furniture. They are of the "same appearance from every angle" variety, leading to a little bit of Nightmare Fuel in the first game with a screaming skull object wrapped in vines that always stares right at you. In later games, every item is in full 3D.
What's especially odd about this is that the pickups that use sprites when seen in the overworld are rendered in full 3D in the inventory.
Star Wars: Rogue Squadron uses animated 2D sprites to render Stormtroopers on the ground in this arcade style flightsim.
Super Smash Bros.. (N64) is a 3D-rendered game with numerous sprites, including nearly all items and projectiles. Some of these, such as the shields or flames, will always face you (even if you pause and move the camera around), while others, such as Fox's laser and the lasersword can be looked at from different angles, revealing them to be entirely flat.
Mr. Game & Watch is a subversion. In Melee" he appears to be a 2D sprite, but he is in fact a full 3D model with no lighting, so from the perspective of the camera he appears 2D. In Brawl'' he is a 3D model with no thickness and several animation sprites (which the game engine probably calculates his flat player model from in real time), giving a flat 2D look, which is emphasized by the fact that the camera does not angle during normal gameplay. On the Flat Zone stages, all 3D player models are somehow flattened into 2D "sprites" in the same manner.
The Battlefield series of shooters until Battlefield 2 all use right-angled sprites for tall grass and other concealment. This is a rude awakening for novice snipers, who happily park themselves in tall grass on hills and plink at distant enemies, unaware that they are not only visible but sitting on a giant X, from the perspective of aircraft.
Battlefield 2 has a minor use of this: weapons are normally polygon models, but when aiming down their sights they become sprites, albeit ones so well-detailed that, except for the US Spec Ops' M4A1 (which magically loses its front sight while staring through its red dot scope), it's nearly impossible to tell.
The old 3D Maze screensaver for Windows: Even though it's not a video game, the maze and multifaceted things that turn the viewer upside down are in 3D, while the Start button, the random hovering Open GL text, the happy face at the finish, and the roaming mice are sprites of the "same appearance from every angle" variety. This results in mice always facing right, which can cause them to seem to walk backwards or sideways despite the optional maze overlay showing otherwise.
Rayman 2 has pickups made from sprites. In the Playstation 2 port (titled Rayman Revolution), however, the pickups are now full polygon models.
The crowd in wrestling games past the first few lines of seats around the ring, still used to this day even if usually pushed back to far rows, some can still be found right in front of the camera during entrances or victory pose such as in Legend Of Wrestlemania on PS3. These, in this case, are not oriented to the camera but in their seat direction which can allow the player to see them as being made out of cardboard so to speak, which gets especially silly in games where you can actually crawl over the divider into the fan's seats and watch said cardboard cutout fans slide away from you.
Legend of Mana features detailed bitmaps for backgrounds and very detailed sprites, but uses the polygon processing power to stretch and distort characters when they dash or shove characters. Beyond that, when using a magic spell that affects a field, while charging the spell, polygons outline the area of effect.
Beyond The Beyond uses this during the battle sequences. It is very painful to watch, since it still uses sprite flipping.
Psychonauts uses this when Raz uses his Clairvoyance power on a friendly character; whenever Raz appears in the other character's view, whatever he or she sees Raz as appears as a 2D sprite in place of Raz's 3D model.
Also, Figments are 2D objects, which can make them hard to see if they're at an angle.
The BIT.TRIP games. The scenery and objects are 3D voxel models, yet most of the characters are Atari2600-like sprites.
Many older racing games use "always facing you" sprites for objects such as trees.
Ys: The Oath in Felghana, and the PC and PSP versions of Ys VI: The Ark of Napishtim. The PS2 version of the latter has 3D characters.
In Cross Edge and Record Of Agarest War, all backgrounds are polygonal, and your playable characters and some of the enemies are rendered as sprites. Most larger foes use 3D models instead.
All distant trees in Just Cause 2 are flat sprites; it's usually not too obvious unless you're flying in a helicopter over a forest, in which case the trees will visibly rotate as you pass them.
Delta Force: Land Warrior uses sprites for all its weapons, meaning playing multiplayer or going into third-person mode would allow you to witness a fully-3D soldier carrying an otherwise fully-detailed gun that was only one pixel wide.
Virtual Hydlide has characters, items and trees rendered as sprites over polygonal backgrounds.
Gradius IV has polygonal backgrounds that clash awkwardly with the old-fashioned 2D sprites. Gradius V has a more consistently 3D look, though the gameplay remains 2D.
Minecraft used billboarded sprites for dropped non-block items before version 1.4.6. After this version, 2D sprites are used only in Fast graphics mode, while in Fancy graphics mode, items are 3D models. Dropped block items are rotating 3D models of the blocks in all versions.
Saplings and other fauna seem to be billboarded sprites, but are actually textures mapped to an X-shaped model, giving the illusion of an intricate 3D model. The texture "flips" depending on what side of the plant the player is facing. This can be jarring if looked at closely, but in normal gameplay it is not noticeable at all.
The Legend of Zelda: The Wind Waker uses 2D sprites to represent smoke or dust (other particles are rendered with a true particle system). What's interesting about the sprites used to represent dust is that the sprites appear to be lit by the lighting engine in real-time, giving the appearance of a 3D model.
Mario & Luigi: Dream Team uses 3D polygons for real-world scenery, Luigi and Starlow during dream sequences, battle backgrounds, and a few other effects, and 2D sprites for everything else.
Utilized in DuckTalesRemastered. Characters are 2D images, but the background and most items are made up of polygons.
Rakugaki Showtime uses this mixture to deliberately garish effect. While the backgrounds are fairly standard 3D, the character sprites are crude pencil drawings surrounded by huge opaque borders.
The way the backgrounds in the early Resident Evil games work is that every room is a simple rectangle or box and textures are used to simulate a believable looking room, including doors (though the few doors that opened that were not a part of a loading screen were rendered as 3D objects). The effect is very noticeable if a monster is killed very close to a wall and their body appears to clip or float through the wall.
Inside most non-dungeon buildings, the whole of Castle Town and the courtyard from The Legend of Zelda: Ocarina of Time, there are entirely pre-rendered 360-degree environments with the camera fixed at a point (and inside buildings a secondary view from above), with polygon-rendered characters on top of it. The game hides parts of character models and faked perspective to allow it to appear as if Link were walking into the background and behind parts of it; these days, the resulting effect looks very weird, especially in emulators, but it is still rather impressive nonetheless. This was probably due to N64 limitations though, as the expansion-pack-utilizing follow-up Majora's Mask, and the 3DS remake of Ocarina of Time, did away with pre-rendered interiors.
Baten Kaitos has several (very bizarre) pre-rendered landscapes.
Troika's computerization of the Temple Of Elemental Evil module uses 3D character models on top of 2D backgrounds, and looks stunningly beautiful as a result.
Total Annihilation is something of a subversion, since the terrain is a 2D image overlaid on a proper 3D heightmap, and the units are plain sprites, onto which 3D models are rendered. This is most obvious with very large units, like the fan-made Beelzebub, which can get clipped against sprite edges at certain angles.
Galaxianł and its spinoff, Attack of the Zolgear use FMV backgrounds and polygonal foregrounds.
Regular stages in Sonic Rush and its sequel, and the DS version of Sonic Colors. The rest of these games are all polygonal.
Grim Fandango and Escape from Monkey Island. Grim Fandango evoke the angular style of traditional Mexican folk art to effectively compensate for its polygonal appearance, but Escape from Monkey Island garnered criticism for abandoning the Disney-like cartooning used in its predecessor.
Commandos 2 & 3. 3 have entirely 3D indoor areas, but the outdoors are still 2D.
Aversion: As noted above, nearly all polygonal games leave the sky up to good old bitmaps. The great wisdom of this practice is illustrated by games like Quake I and Deus Ex, which have an incredibly ugly sky made of one or more layers of giant polygons.
Skies used in modern games are, in fact, polygonal spheres or cubes without lighting, textured with images of the sky and other background elements.
Quake also has very ugly polygon flames when compared to the natural-looking (except from above) flames of Unreal. Note that Unreal's flames aren't sprites but rather two flat polygons at 90 degrees of each other with flame textures on them.
A non-game example: Microsoft 3D Movie Maker uses bitmap backgrounds with a built in depth map so that you can place 3D models anywhere in the scene and have them appear properly occluded by foreground objects.
Averted when people started making their own backgrounds by combining 3D objects together.
The titular dancing Elite Beat Agents are rendered in 3D during gameplay, but the rest of the game (backgrounds included) is hand-drawn.
Also used in Odium (originally Gorky17), where it was painfully obvious.
Honorable mention to Mega Man X2. It has a similar chip to the Super FX built in, but it was used to render vector models over the sprite backgrounds, many of which are at least in spirit wireframe models, though untextured and monochrome. Mega Man X3 also uses the chip, though it has the same limitations.
Command & Conquer: Tiberian Sun and Red Alert 2 have isometric backgrounds/buildings and voxel 3D vehicles.
The N64 port of the original game has 3D models for buildings and vehicles, but keep sprites for infantry.
The Sega CD remake of Silpheed uses a rather odd method; while it appears to have a polygon foreground and background, the background is actually a pre-rendered streaming video, essentially having the whole game take place on top of a rolling Cut Scene. Some games such as Microcosm belong in the section below for using sprites on top of the rolling pre-rendered FMV instead.
The Fear Effect games also use FMV backgrounds and 3D characters.
Older 3D fighting games, such as the first few Tekken games, use 2D backgrounds.
The first installment of The Sims uses 3D characters on top of isometric 2D backgrounds.
Again, the first Star Fox game, but this time it's the planet/space scenery backgrounds which are fully 2D, with some tilting and occasional distortion effects. The ground has to appear especially featureless so it would stand in as any generic ground.
Zaxxon's Motherbase 2000 has polygonal ships and other enemies over flat-looking diagonal-scrolling backgrounds.
The Sega Saturn game Shining Wisdom was originally going to be released on the Sega Mega Drive but was hurriedly ported to increase the number of titles on the system. The result is that the 2D backgrounds are the type of thing you would expect to see on the Mega Drive while the characters are 3D sprites that would later appear in Shining Force III.
Mixed and Other
In Radiant Silvergun, the 3D, 2D and pseudo 3D is all over the place. Both 2D and 3D can be found in foreground and background.
Deliberately done in Darwinia. Darwinians, basic virii and many other objects are 2D sprites while rest of the environment is 3D.
A rather bizarre example in World of Warcraft, which has a stack of cannonballs scenery object that is made up of rendered polygonal cannonballs displayed as sprites.
Many weapons in the game have little embellishments on their hilts (small pieces of cloth, a ball tied to a string, so on) that are sprites of the "same angle no matter where you look" variety.
Viewtiful Joe is a rather prominent example, with 3D characters and backgrounds and 2D props, pickups and occasionally enemies scattered throughout.
The 3D game Bug! and its sequel Bug Too! have 3D platforms and terrain, while the characters and Mooks are 3D rendered sprites.
The Ace Attorney series consists of 2D sprite-based visual novels, however some of the games let you view certain pieces of evidence in 3D. As of Dual Destinies all characters and scenery made the leap from sprites to models, but evidence is still largely presented as sprites.
In many of Valve's games like Half-Life and Left 4 Dead, nearly everything is rendered in polygons, but plant objects like shrubs and clumps of grass are rendered as sprites.
In Half-Life, those aren't sprites, but rather extremely (1 unit) thin boxes with a plant texture on the 2 big sides and an invisible texture for the thin ones.
Azure Dreams has pre-rendered sprites on fully 3D backgrounds.
The original Crash Bandicoot trilogy has this for, obviously enough, wumpa fruits, as well as several visual effects or the "CHECKPOINT" letters. And yet the spinoff, Crash Team Racing, brings more 2D/3D confusion to the desk: the wheels, the smoke, the vortex and the wumpas are all sprites, but the race position numbers are actually 3D models.
The first three Inazuma Eleven games have both 2D sprites and mugshots and 3D models of characters. Closer-up camera angles use the 3D models, while distant angles use 2D. Backgrounds are also 3D except for directly-overhead camera angles, which use a 2D background for the ground or floor.
The backgrounds in Skullgirls are a mostly of 2D art but laid out on a flat polygonal plane in some cases.
The Jimmy Neutron videogame adaptation has polygonal graphics for everything except the various collectible items, which are sprites. The fact that they are high-resolution enough to look like photographs in comparison to the somewhat archaic (even for the time) graphics makes the juxtaposition somewhat jarring
Everything rendered in Second Life are completely 3D, but the default trees have leaves rendered on a flat plane, similar to the cardboard effect used in other games. Users can also create content that act like sprites, but are 3D objects flattened down. Turning on the avatar imposters option can turn people you see into choppy animated 2D sprites if there are too many avatars on the screen at once.
Microsoft's Flight Simulator 2002 is completely 3D - except for clouds. Setting the view mode to Top-Down shows that clouds are actually high-resolution sprites that always face the aircraft, giving the illusion of fully volumetric clouds.
Most of the graphics in the UbiArt Framework-based Child Of Light are 2D, with the exception of some 3D models like Aurora, Norah, and a few others. This extends to the earlier Ubi Art-based "Rayman Legends" and possibly "Origins".
Wonder Project J2 for the Nintendo 64 is almost entirely 2D sprites and backgrounds - with the exception of part of the intro cinematic, some action sequences (3D backgrounds with a 2D character sprite), item display in shops, and the world map. The 3D action sequences are considered to be the worst part of an otherwise charming and great game, as they control horribly and look like something out of the SNES's later 3D games, just with slightly higher-res textures and more polygons.
Another non-video game example: Despite Space Engine's extraordinary beauty and realism, it uses 2D sprites to render nebulas and other cloudy objects. Occasionally the user can see rotating sprites when he or she rotates the object, ruining the immersion the graphics otherwise gives. This is barely noticeable in normal usage, however.