Yes. You can play any Pokemon game for DS on a 3DS. Although unfortunately, it will not be 3D like games designed specifically for it. Solumni provided a list of almost all the Pokemon games compatible with 3DS, forgot X and Y >:D. Only Generation 4, 5 and 6.
But it should be noted that you can't play Game Boy games though, as only the DS Lite has a spot for the cartridges (DSi doesn't have it either D:). This means games that are Generation 3 and below, Ruby, Sapphire, Emerald, Fire Red, Leaf Green, Silver, Gold, Crystal, Blue, and Red cannot be played on a 3DS.
Hope I helped! :)