Final Fantasy VI had a few dinosaurs as random encounters. It also has Dinosaur Island, a place which does not provide any plot or gameplay bonuses, but has a lot of tough fights which are good for levelling up.
Also don't forget that in Red Alert 2's expansion Yuri's Revenge, the first Soviet mission deals with time travel and you're accidentally sent back to the dinosaur period to fight off hordes of T. rexes. This of course includes the fate of the game's antagonist Yuri in the same campaign who after stealing the time machine from the Soviets tries to use it to "command and conquer" the world and all its history. Unfortunately for Yuri, the Soviets still had the command codes for the time machine and depleted all of its energy reserves to send Yuri back to the dinosaur era while he was gloating. Then Yuri lets off a Big "NO!" as a T. rex smashes through the time machine to devour him.
The first Tomb Raider game had dinosaurs and a T. rex as enemies for no particular reason other than Rule of Cool, though an FMV later in the game implied that they were created by the Scion. The dinosaurs returned without explanation in Tomb Raider 3.
Tomb Raider 2 and its Gaiden GameGolden Mask both feature secret, difficult-to-reach battles with more T. rexes, the sole reason being that they were considered the coolest part of the first game.
Turok would just be another FPS if it didn't pit you against dinosaurs.
World of Warcraft has Raptors as fairly common animals (and mount for trolls), and gigantic T. rexes, called Devilsaurs, as a rarer sort. To be precise, they only appear in a few areas (Un'Goro Crater, where there are only about five of them at any given time; The Netherstorm, where a single Devilsaur rules over an eco-dome filled with raptors; Drak'Tharon Keep, with the optional boss King Dred; and Sholazar Basin, home of the rare-spawn King Krush). For being such enormous beasts they move like ninjas, and many players have had their adventure cut short by a sneak attack.
With the latest patch, Beast Mastery Hunters can tame one of these giants (although it inexplicably shrinks to a more manageable size in the progess). It's undoubtedly the coolest of the exotic class pets (although that isn't saying much when the competition consists out of prime choices like bugs and worms).
There are also Dragonspawn, bascially flightless dragons.
With the reveal of patch 5.2 in the Mists of Pandaria expansion, World of Warcraft is taking it Up to Eleven. The Zandalari trolls have revealed they have dinomancers, complete with Devilsaurs, Triceratops, and Pterasaurs. All of which have awesome armor, and some with cannons strapped to their sides. Say it with me again: Dinomancers. You wish you were that cool.
Guild Wars introduces a dinosaur-rich jungle in its Eye of the North expansion. Being a fantasy game, it includes feathered Raptor Assasins, Armor-plated ceratopsians with shoulder-horns, Tyrannosaurs, therapods with multiple heads and tails, and other bizarre reptiles.
The Super Mario Bros. series of games already had Bowser as some sort of dragon-dinosaur-turtle... thing, and then in Super Mario World along came Yoshi and his friends....
Not to mention the cute bruiser herself, Birdo.
Pokémon uses several dinosaur and related species-themed Mons over the years: Lapras (Plesiosaur), Aerodactyl (Pterosaur), Tyranitar (Godzilla with some hints of T. rex), Meganium (Diplodocus or other sauropods)), Groudon (vaguely T.rex-ish), Torterra (an ankylosaur crossed with a tortoise), Cranidos/Rampardos (Pachycephalosaurs, not T. rex), Shieldon/Bastiodon (Triceratops or other ceratopses), Rhyperior (an ankylosaur crossed with a rhino), , Archen and Archeops (Archaeopteryx), Amaura and Aurorus (Amargasaurus) and Tyrunt and Tyrantrum (very unambiguously based on T. rex).
Another Source Mod, Jailbreak, has this as part of the premise: It's DinosaursvsRobots.
The Monster Hunter series features raptors as mooks. With the sequels and updates, you are getting a lot of dinosaurs (that happen to be changed slightly) that stand out. There may be odd hybrids and creatures that are outright dragons but the sheer number of dinos in the series is definitely worth looking through. That and the giant T-rex that Monster Hunter Tri introduces to you all.
Dwarf Fortress sends goblins after you. Survive long enough, and they come mounted on velociraptors (known in-game as Beak Dogs).
Chrono Trigger's dinos actually appear in 65 million BC (along with people, oddly inverting that trope) as well as in a 600 AD bonus dungeon (where millions of years of underground living have made them tough as nails).
There are also dinosaurs that can be encountered as monsters. While their inclusion is justified since the jungles of Chult are famous for them, they aren't important to the plot here any more than any other random monster. There are a couple of minor quests involving them though.
Fur Fighters had the characters discover a whole advanced society of Dinosaurs living under the surface of the planet. The plotline had something about the Big Bad stealing the advanced technology and selling it for cash but it didn't really work out. Oh, and the heroes were on a popular children's TV show for some reason.
The krogan from Mass Effect are vaguely dinosaur-like. The first Krogan you recruit as a party member is even named "Wrex." The turians are also described as resembling the link between dinosaurs and birds.
In Mass Effect 3, a Side Quest provides salarian scientists with an alien dinosaur's skull. They clone it, Jurassic Park-style, giving your krogan troops dinosaurs to ride into battle. Sadly an Offscreen Moment of Awesome as we never manage to see the krogan using them. A shame!
Champions Online, being inspired by nearly every generation of comic books ever, has Monster Island - the western section of Monster Island is covered with raptor-sized "Teleiosaurus hatchlings" of various kinds, and the island is also home to the ginormous (30-40' tall) Teleiosaurus, a dinosaur egg several stories tall, and Mega-Terak - a ROBOT dinosaur.
Learn Special Relativity with Velocity Raptor! She can run at 90%c! (Or more correct, the evil Professor Rex can reduce c to about the running speed of Velocity.) You'll soon learn that running at 90%c has certain unwelcome effects...
The "snappers" and "razors" from Gothic look like small T-rexes, only without any arms. The "biters" also resemble dinosaurs.