Legendary Axe I & II. Mandatory. The "sequel" will probably have more initial appeal, but the the "original" rocks hard as well.
Devil's Crush, if you like Time Cruise and want some more pinball.
Bloody Wolf, if you want to save the president of the U.S. (the goal of any worthwhile Data East game).
Air Zonk if you like the Bonk universe and want one of the cutest horizontal cute-em-ups (shooter).
If you dig the old-skool SSI Dungeons & Dragons games, then definitely get Order of the Griffon. It captures their spirit well, which is kool for a conversion to a console. Trivia: Black_Tiger will probably be able to verify this, but I don't think OotG appeared on any other platform? At least I don't remember seeing it for the PC or C64.
Timeball, if you want to see a puzzle game that many folks loathe, but that I find enjoyable (seriously though, get other puzzle games first!).