Well, I’m breaking my “no classic games” rule with, in this case, Super Mario Bros 3 – the 3rd game in the series (duh), and in my opinion, the second best (after the first game). In addition to having the video up on YouTube, I’ve got the video (in a hopefully higher quality version) uploaded on Megaupload.
Super Mario Bros. 3 is also available on the Virtual Console. You can also get it on eBay of course, either as the NES game (or the Game Boy Advance port if you’ve still got a GBA or a DS or DS Light (DSi users will be in a bit of trouble through), or in the form of Super Mario All-Stars for the SNES. If you don’t have a SNES or a NES already, or have a HDTV, I’d recommend the Retro Duo SNES/NES System, just because it will talk to your HDTV a little better than the original NES or SNES would. It doesn’t necessarily upscale, but if you don’t already have the composite cables or S-Video cables for the SNES or NES already, you can hook them up to your HDTV without having to play with funky adapters.