I'm going with the GP2X, and I can't mention my game of choice without descending into a bit of rambling praise for the developer and the rest of his work.
My favourite game on the system is
Sleuth Slots, by Ruckage. It's a reproduction of an old school slot machine, with a very camp Cluedo theme. The aim is to identify the murderer, murder weapon and location of the crime, which unfolds through various features and minigames. It's all chance of course, just like a real slot machine. But the music is on point, the artwork is fantastic, and the action is frantic and hilarious. I've whittled away many hours playing it over the years, and it still makes me crack a big grin every time I play.
The world has changed since then. The rise of mobile gaming means you can find a million cute little pick up and play titles, and I expect a lot of people won't think much of these offerings at all. But in the GP2X scene, where homebrew ruled and everyone knew everyone, Ruckage brought a level of polish to his releases that was very rare. You don't own a GP2X without his catalogue on your SD card.
Some more:
Dastardly Dungeon: An extremely faithful Game and Watch tribute, in the form of a multi-screen roguelike.
Animatch: Zoo Keeper, basically.
Protozoa: Sciency snake game with excellent synth music.
Snake on Dope: Another snake game. In this, you get more stoned as you go, and the screen wobble effect ramps up. Backed up by a synth-cover soundtrack of classic stoner music (Marley etc), and funny little stoner sayings every time you 'level up'.
Ruck-Man: Before PacMan CE, we had this. Another excellent take on a classic.
Space Varments: Tap-to-splat alien killing game, with a very comical Mars Attacks vibe.
There really needs to be a Youtube video to showcase these excellent pieces of homebrew history.