I think the official Mega Wide Gear magnifier is great. It makes the GameGear look like one of those old high-quality cameras. And since it's fully boxed in around the sides, it prevents extra light and glare from entering, so you get a clearer, crisper display.
The game genie is also a must (for any system).
The TV-Tuner is the Beamer of the game-gear periphenalia. I can't say I've really needed to use it ever, but it's just fun to whip it out in public and start surfing for receptive channels (at least until the networks go all-digital).
A Car and AC-adapter are also required, so you don't have to run through batteries like mad. A battery pack would also be nice, but make sure you buy one that's new. I tried some used ones, and they're all worn out and won't hold a charge anymore. Remember that reduced capacity on rechargable batteries is not a result of not letting it drain completely before recharging. It's a result of over-charging. So make sure you time it and unplug the charger when it should be done.
Oh yes, and a pair of headphones.
I also enjoy the Sega game-gear briefcase. It holds the GameGear, all the accessories, and 12+ games.
Check out Tails Adventure. It's a really good old-school adventure game. I don't usually get into adventure games too easily, but I played this one for days until I beat it.
All the normal-sonic games are also fun. Sonic The Hedgehod 1 and 2 are different from the Genesis versions (I think they're the same as the Master System versions though?). Chaos and Triple Trouble are great. Blast is really slow and has awful collision detection, and Labyrinth is isometric and not too fun.