The 3DS does play (almost) all original DS games, including both physical releases and DSiWare.
There are two Mario platformers on 3DS, Super Mario 3D Land and New Super Mario Bros. 2. I think both of them are really good, though I'd recommend the former over the latter. As for other things, there's a lot of variety, and I'm not sure what you'd be interested in. Fire Emblem: Awakening is very good, if you like strategy RPGs. If you never played Donkey Kong Country Returns on Wii, the 3DS version is easily the best way to play that great game.
There's also a lot of great downloadable games on the system, with stuff like Mutant Mudds and Mighty Switch Force being great, traditional experiences there.