For sure go for LoZ: Link's Awakening. DX version or be a bad-a and just rock the original version.
As far as GBC goes, the Mega Man Xtreme games are pretty fun. Game & Watch Gallery games are certainly charming and guarantee some fun if you're not wanting to invest any time. All the RPG suggestions are surely great. Here are a few games I remember playing that I really enjoyed:
GB: Battletoads. Do it.
GBC: R-Type DX, Blaster Master, Game & Watch Galleries, Wario Land 2/3,
GBA:
- Mario & Luigi: Superstar Saga - freaking amazing. So fun and hilarious.
- Sonic Advance (only played the first one, but I assume they are all above decent. Loved the pace and visuals of sonic advance vs. other ports).
- The Donkey Kong Country ports are all good as are all the Mario Advance games.
- Gunstar Super Heroes.
- Super Street Fighter 2 Turbo REVIVAL (yes this is just the name of one game).
- Advance wars?
- Mega Man Zero 1-4
- Final Fantasy (any)
- Sword of Mana
- Mario Kart Super Circuit - I still enjoy this game
- Kirby: Nightmare in Dream Land and The Amazing Mirror are both great
- Golden Sun?
I dunno a whole lot of super obscure titles or anything, but I was fortunate enough to find out that these games are great.
Now, as far as DS goes, I have a personal list of games that I think every DS owner should at least play once.
- Elite Beat Agents - in any given clearance bin. Worth at least one playthrough for it's hilarity.
- Any game from the Scribblenauts franchise.
- Kirby SuperStar Ultra. Not just a port, but an elaboration of the game itself. Goes beyond what the snes version offered while keeping it intact. It's the best Kirby game in my opinion and easily the best one to play with a friend.
- Mario & Luigi. Both games (partners in time and bowser's inside story) are hilarious and sport the same tried and true yet rewarding battle systems as the GBA title.
- Tetris DS is awesome. Just sayin'
- if you get a dsi or 3DS, be sure to get Cave Story. It will likely change your life.
- Chrono Trigger. If you want...
- Lunar?
- Dragon Warrior?
Well I've pretty much exhausted my personal experience. I could start naming titles I'm sure you'd enjoy, but I'm trying to give you a some suggestions based on stuff I've actually played and enjoyed.