My first PC game was Recoil which came with my families first PC back in 2000, it was pretty fun for a tank game with 9 or so different pickup-able weapons with some alts and 3 other forms for the tank such as boat, sub and hovercraft, but unfortunately it was very obscure because of the large range of games available at the time. I was 13 at the time I first played it.
My first handheld game was Super Mario Land which came with my Gameboy Pocket, and my first console game was Super Mario Sunshine which came with my Gamecube.
For me with first played it was:
PC: Either Descent or Lode Runner on an old school PC
Handheld: Either some Power Rangers LED game device or Tetris game device.
Console: Sonic & Knuckles on my brothers Sega Megadrive or a 32 in 1 game on my brothers older Atari system.
Ahh, the memories. My first experience with video games was without doubt my parents' pong console, 1983 or so when I first remember it, hooked up to our B&W TV.
After that, I'm not so certain between a small LCD "catch the object" type of handheld, arcade games (I remember Bubble Bobble vividly) and my cousins' Amstrad CPC computer (all around 1986-1987).
I also had (and still have) one of those:
If we're talking about systems that I owned personally (and not played at other peoples' houses, at the arcades or borrowed), then my first PC games would be some old XT games (Hard Hat Mack etc.) given to me by neighbours when I got my first very own PC, in Summer of 1994. Doom came shortly afterwards. My first "true" console in that sense (not tabletop or LCD single-game) would be a Famiclone I got in 2002.
My first handheld game was definitely Pokemon Blue on a Game Boy Color, my first console game was Donkey Kong 64 on the Nintendo 64, and my first PC game was Mortal Kombat on the MAME emulator (if I remember correctly). Good times!
EDIT: I actually lied about consoles. For some reason I thought about PSX and everything after it... when I played Pegasus games before (Pegasus was our local NES equivalent, dunno if it was sold abroad) and I believe "Contra" was my first console title ever.
First PC game was at an uncle's, on a green screen monitor of some sort... You flew a helicopter and shot little dudes in buildings and things... Can't remember much aside from that, but I was pretty enchanted.
Probably the first game I really got into was a crummy little handheld version of Bad Dudes that my grandparents got me for my eighth birthday. Then there was a Space Invaders handheld... then some time after, an actual NES. o_O;; My little boy mind was blown, even if I did play it on a black & white TV.
PC: Lombard RAC Rally. I didn't think much to it. Home computer though, years back, was my Amstrad CPC464 and Chuckie Egg. Still an amazing platformer.
Handheld: Motorcross Maniacs on Gameboy.
Console: Ghost House on Sega Master System.
The latter probably made most of an impression on me, and may be responsible for my flair for cartoon-spooky.
PC: maybe that DOS port of Golden Axe in 1997.
I've never seen a handheld/console in real life but played some games on emulators, the first was probably Golden Axe too (wanted to play it again after like 8 years but couldn't find the DOS version or couldn't figure out how to run it).
Not sure, it's been so long. Also depends on wether it's my first owned or my first played.
Atari ST: (Though technically this is a PC too) I got a few games when I bought it, But the one I played most of them was probable F-29 Retaliatior.
PC: Maybe it was Midwinter 2.
Handheld: Only ever owned one, Doom 1 on GBA.
Console: I think it was when I got Dynasty Warriors 2 from my sister and her Boyfriend. But I never bought a PS2. So their plan to make me get one failed.
Atari ST: Rick Dangerous
PC: Either it was Sim City or it was Klondike/Solitaire (the card game that comes with Windows, not sure whaty it was called in English)
Handheld: Probably Tetris. My friend had a kind of game system that you could carry with to school once that I tried, but I dunno if it can be called a handheld. But if is, then I suppose it was Pong.
Console: Either it was Super Mario Bros or Ice Climber.
I may not be the oldest guy here, 33, but these are almost impossible to remember! My first console was Atari2600, and I remember having a handful of games, but no idea what the first was - could have been Pacman, Pitfall, Demon Attack, Moon Sweeper, Combat, Jungle Hunt... you get the idea.
First PC games wasn't as long ago. We had an Amiga 500 before a PC, and it was around 1991 when we got a 486, I think. First games I remember playing, Quest for Glory 3, Kings Quest V, uhhh... drawing a blank. I remember, most of all, getting a modem and getting every shareware game we could find from BBS boards, which was the eventual path to DOOM!!!
First handheld? Unless we count shitty Tiger games, that's an easy one! TETRIS, MOTHERFUCKERS! :)
Console: PSX Doom and also the second game I ever played and no, I am not joking.
Hand held: Zelda Link's Awakening DX or Pokemon Yellow (I can't remember which one as I got these with my GBC on my fourth birthday along with Wario Land 3. One of these was my first experience in video games, (we were poor at the time so couldn't afford much, until my step dad came along which in turn brought Doom into my life for the first time).
PC: Unreal without a doubt one of my all time favourites I wasted many a time on that.
PC game: I suppose it would technically be one of the games I had for my TI-99/4A, like Tombstone City. But I treated that computer more like a console. As far as x86 machines go, either Lode Runner: The Legend Returns or The Even More Incredible Machine. They had come pre-loaded with my old Compaq.
My first PC game was The Adventures of Captain Comic - specifically, the old version that played the US Army Hymn when it booted up. In glorious one-channel beep.
My first console game was on my Dad's Atari 2600, but at that time I'd had so many choices for games that I legitimately can't remember if the game was Wizard of Wor, Laser Blast, or Circus Atari. Maybe it was Dragster.
My first handheld game was in 1992 or so when I received my first Game Boy for Christmas. So the game in question was, appropriately enough, Tetris. Nowadays I'm pretty much tired of Tetris, though. =P
PC: Hell if I know. Probably some of those old Sesame Street sites you could access over Prodigy. Maybe Cosmo's Cosmic Adventure. Maybe Soleau Software's Ladder Man. I also recall a really-early tile-based game where you could modify the tiles in an art editor, which I then used to make purple-and-green tiles which I felt oddly proud of, but I can't remember the game's name for the life of me. I was really young when I was playing PC games, so my memory hadn't fully formed.
Console: Still not entirely sure. It was probably an NES game, since that was apparently my gift for my first birthday... probably Super Mario Bros. or Duck Hunt, as such, but again, memory hadn't formed.
Handheld: This one I'm more confident about. It was either Sonic 2 or Land of Illusion: Starring Mickey Mouse for the Game Gear, since the Game Gear was my first portable and those were the games I got with it. I'm pretty sure it was Sonic 2, which was, in fact, my first Sonic game ever. It's a total wonder that I stuck with the series with such a crappy introduction to it, given the first zone's boss is still practically impossible, even for my 25-year-old self. The boss is fair enough on the Master System original: there's some sort of antlion robot doing sweet FA in the lower-right corner that you can't hurt, while Eggman is dropping bombs on to a downward-slanting hill from the upper-left; dodge the bombs (which always have the same arc, but where they touch the ground shifts a bit), which will eventually destroy the antlion robot and you can continue. The Game Gear version added more randomization to the bombs' arc (wide/short or thin/tall), so you're not sure what to expect, and then shrank the arena because of the console's smaller screen, so you have even less time to anticipate them. The end result is a pure guessing game that you have to be correct 6-8 times in a row with to win, because like hell you'll have enough time to react to them naturally.
ROCK & LOAD COCK BEEN BLOWED IN YOUR MOUTH, MANJUICE EXPLOAD
First PC game: Too long ago to remember specifically... but probably some arcade port on the Commodore 64. Console game: Asteroids on the Atari 2600. (Technically, the first game I played on the first console I owned was Super Mario Bros.) Handheld: Do Game & Watch games count? If not, Tetris on the Gameboy.
PC: JetPac and Doom (at that time Doom and More CD Shareware).
Console: If for me alone, it was Nintendo 64 with LoZ: Ocarina of Time, Duke Nukem 64 and Doom 64. But for firsties, Super Nintendo with LoZ: A Link to the Past.
Handheld: GBA with Mario and Luigi: Superstar Saga.
Why don't I have a custom title by now?!
If I may take the definition of "PC" even further than kristus, my first game was probably typed into a borrowed VIC-20 from a magazine listing. Might have been Depth Charge or a City Bomber variant, can't say for sure after 30-odd years.
My first handheld is just as old, a Space Invaders clone with a matrix of LEDs behind a smoked perspex screen. Still have it and can post a picture later if someone wants a laugh.
My first console is even older, a Sheen M-1200 from the late 70s which has several built-in games, with Ten Pin Bowling probably being the one most played. It's in the garage.