I gravitate towards artsy or comically dark games mostly, for example Mother 3, so yeah.
1.
Cave Story(WiiWare). Represents everything good about NES and SNES 2D platforming. It's got a quirky premise, and good writing for that kind of game. You can download the PC version for free, but the WiiWare version costs as much as an MW2 map pack(lool) and you get a lot of new stuff out of it. All three difficulties are just right. The remixed soundtrack and improved graphics are nice too, it's just a shame there's no sound test.
2.
Majora's Mask(N64 VC). I had rented this game when it was out for the N64, but never got into it. I was waiting for the VC release for a long time, and was stoked to finally play it. I said I'd write a review for this earlier, but never got around to it. So let's get right to it: personally, I think Majora's Mask was the best Zelda game of all time. OF ALL TIME. I'm gonna compare this game as a sequel to OoT; it really shows how creative developers can get, with a smaller team working with the old OoT engine and character models to create an entirely new world. The writing is great; the NPCs' actions are a lot less mundane and you have to interact with people a lot more, yet the time system retains that world on your shoulders feeling there is in Zelda. Better than Oblivion's NPCs for reference, haha. They replaced Ganon as a villain really well, but I won't spoil anything. The tunes are usually a lot more varied and catchy. The difficulty is a level above most 3D Zelda games, but if you've played Zelda a lot and can use the ingame maps then you shouldn't need a walkthrough.
3.
Kirby 64: The Crystal Shards(N64 VC). This game needs extra patience to appreciate, even for Kirby. The difficulty is too low. What this game is remembered for instead is its also delicious
soundtrack, cult followed characters, and visual method of storytelling ala Brawl.
4.
Donkey Kong Country 2(SNES VC). Great game throughout, but I could never finish it. Damn retro difficulty. Good soundtrack, do I see a pattern here? If anything I'd tell you to listen to the K. Rool battle theme, Mine theme, and Bramble Blast theme on Youtube and make you decide from that.
5.
Mega Man 2(NES VC). Good Mega Man game to start with. Easiest of the originals, but still more enjoyable if you use save states haha ;_;. Sounds like Mega Man.
6.
Super Mario RPG(SNES VC). Fun game with a cult following. Non-traditional JRPG with about as much platforming as leveling. Anyone can enjoy it to some degree.