Barkley, Shut Up and Jam: Gaiden is a fully playable 16-bit JRPG-like game that parodies the genre. The game is quite a bit less affectionate with its parody of the RPG Maker community and certain Internet subcultures in general—two of the "truck pump" rants that you read before saving are taken verbatim from real Internet discussion forums, although one was a reaction to one of the made-up rants that the author confused with the real thing.
The RTSMajesty puts the player in charge of a fantasy kingdom that works the way they do in RPGs. As such the city guards are helpless against anything bigger than the giant rats infesting the sewers, and the sovereign has to summon heroes (who are not directly controllable units) and post rewards for things like the ancient evil castles littering the landscape in order to get anything done.
Viewtiful Joe affectionately parodies the plots, characters, and settings of Tokusatsu and Comic Book heroes in general, with the gameplay being a highly enjoyable twist on 2D beat-em-ups.
The Wii game MadWorld, a spiritual successor to God Hand, continues its ancestor's stint of parody by turning the focus from Japanese entertainment (videogames and anime) to western entertainment (gory, violent video games, reality television and graphic novels), sending up their violent tendencies in a comedic, Tom and JerryItchy and Scratchy kind of way.
Anarchy Reigns: Though seemingly very strait laced in terms of story, but characters are definitely parodies. You have 3 assassin chicks and the only serious one is RinRin, the other two are very... odd, one being a gambling and self-absorbed chick obsessed with her beauty, the other is a hyperactive girl who makes Funny Bruce Lee Noises and breaks her gaming system for losing. The main characters of the story are much more serious, but side characters are clear parodies, sometimes of the expected type of character to be in a fighting game.
The Tex Murphy games: Every plot element from old-school, black and white, noir private eye films are lovingly re-created and mocked.
The Leisure Suit Larry games started out as classic parodies of the text-adventure games their own company was famous for, most particularly their less-than-family-friendly Softporn Adventure. Lowe pretty much took the whole thing and did a Tone Shift, playing it all for raunchy laughs.
Likewise, many of the Sierra "Quest" games (King's Quest, Space Quest) spoofed fairy tale or sci-fi tropes. It was a bit more tongue in cheek in King's Quest, but Space Quest was nothing but rapid-fire sci-fi jokes.
Konami's aptly-named Parodius series is a parody of one of their own series. What series, you ask? You have ten seconds to guess.
Konami also parodied its own Castlevania series from the 8- and 16-bit era with the Kid Dracula series. Kid Dracula himself appears as a character in one of the Parodius games.
After Parodius, other companies made silly versions of their most famous shoot'em up series. For instance, Taito mocked Space Invaders with Akkanvader (AKA "Space Invaders: Attack of the Lunar Loonies"), Namco spoofed Galaga with the Cosmo Gang arcade game and Hudson Soft made fun of the Star Soldier series of games with Star Parodier.
In a similar vein, Metal Wolf Chaos is From Software cheerily mocking the everything-to-eleven spirit of anime, flag-waving American patriotism and their own Armored Core series. They clearly love all of these things.
The Disgaea series frequently parodies anime and its cliches. Captain Gordon, Defender of Earth! is a parody himself.
And anime-series featuring toys as their main selling point, like Beyblade.
As well as a few jokes at Square-Enix's (the game's producer) expense, such as the character designer's obsession with zippers ("Then I wish I had more zippers, so I could tell you to zip it!") to your common emo RPG protagonist ("Must...resist...emo...urges..."), and even a joke about yaoi fangirls (which create a significant fraction of Square-Enix fanfiction).
Serious Sam is not-at-all serious, but a self-conscious send-up of FPS games that spread itself across other action game and film sources, and parodied Duke Nukem with particular affection.
The Merry Gear Solid games, particularly Merry Gear Solid 2. They're really scathing and attack with pinpoint precision all of the silliest things about an admittedly pretty silly series, like the ridiculously convoluted plots and turgid infodumps, but the sheer dedication to getting everyone In Character and replicating the Original Flavor of the Metal Gear series is what's most noticeable. The games even take stabs at morals and postmodernist fourth-wall wankery. As well as Christmas-themed Hurricanes Of Puns.
Metal Gear Solid 3: Snake Eater, in typical Metal Gear fashion, is both a parody and a homage to James Bond movies. The game even starts with a typical Bond opening scene which ends in a climactic explosion that turns into the extremely bond-like intro movie. Then the actual mission of the game begins back in America where Bond Snake receives his briefing. Back behind enemy lines he makes contact with a Soviet double agent who turns out to be the game's Bond Girl.
The Grox from Spore are a spoof pastiche of the Borg from Star Trek: The Next Generation (with their cyborg limbs) and the Daleks from Doctor Who (with their war cry being "EXTERMINATE! EXTERMINATE!"). However, some of their threats are less then effective. ("You will not get a holiday card this year.")
Fur Fighters last hub is just one big homage to James Bond, with secret volcanoes bases, stock-piles of gold, a duo female fighter force consisting of a deer and a rabbit and a small little bald man...being petted by a large white cat.
Indie game Indistruc 2 Tank's story mode is a massive parody of Metal Gear Solid, but there's a little too much genuine heart in there ("Give me...a soldier's death!") for it to be a proper skewering.
Sonic Colors is an affectionate self-parody, making fun of Eggman's robotic skills, Sonic and Tails' approaches to being a hero, and 3D Sonic in general. In doing this, is it is a fairly pointed, but affectionate, Deconstruction.
Duke Nukem 3D is an affectionate parody of Doom, combining the latter's over-the-top violence with Black Humour such as turning the LAPD (or LARD as they are in the game) into literal pigs.
Brutal Legend both celebrates and parodies stereotypes associated with Heavy Metal music. It was made by veteran video game designer Tim Schafer, who has been a fan of heavy metal since he was a teenager.
The Flash game Pretentious Game gently pokes fun at the conventions of pretentious puzzle-platform games like Braid and Limbo (and the many imitations they spawned) while at the same time being a pretty good example of the genre, using gentle music and minimalist game-play and graphics to tell a story of unrequited love.
Double Dragon Neon is not so much a love song as it is a power ballad to beat 'em ups, the Double Dragon franchise, and the 1980's all in one awesome package.
The Never Hood parodies the Creation story in The Bible. Given that Doug TenNapel is himself a Christian, the "affectionate" part is easily understandable.
There's a tale in the Bible about a man named Joseph who saved his reputation by being able to interpret dreams; one character (Klee) mentioned in the Hall of Records does the same by reading portents in people's bedhead.
There’s also a reference to the tactic Joshua/Jesus Nave used to conquer Ai.
Let's just say that a great deal of the Hall of Records is a Shout-Out to one Bible story or another.
they turned trembling to one another, saying "What's up with that?"
Resident Evil 4 manages to parody it's own series. The Resident Evil series serves as one of the cornerstones of survival horror, but the fanbase regularly makes fun of many of its quirks and flaws. The developers of 4 tried their best to embrace as many of Resident Evil's more memetic issues, including its comically atrocious writing and voice acting as well as the utter absurdity of the game's premise itself. Previous games were known for their Narm caused by their complete seriousness in the face of glaring literary flaws, but with 4 the developers deliberately went for the Narm Charm route and ended up producing an enjoyable game that didn't hesitate to poke fun at itself and its history. For instance, while the "master of unlocking" line was unintentionally funny in a cringingly bad sort of way, the "Your right hand comes off?" line can't help but be deliberate in its corny hilarity.
Team Fortress 2 is an Affectionate Parody of FPSes in general. The objective of the land war is seemingly completely pointless, the setting is gleefully demented, and each of the nine classes are Player Archetypes painted with a very broad brush and ten coats of crazy.
Dragon Fable is packed with these. A random example would be the quest boss "Puce Person Eater", which, you guessed it, is one-eyed, two-horned and purple. The item description follows the lyrics almost to the word.
Syobon Action is an affectionate parody of both Super Mario Brothers and stupidly difficult platformers, while also being an excellent example of a stupidly difficult platformer itself. Part of the fun is finding out just how creative the devs got in their attempt to make the game absurdly hard, so you will encounter several traps that are so ridiculous and unexpected you have to laugh.