The 90's were dominated by the Super Nintendo and Sega Genesis in the first half, and then the N64 and PlayStation in the second.
For the Super Nintendo, the safest bet for a good time are the cornerstones Super Mario World and Super Mario World 2:Yoshi's Island.
For the Genisis, Nothing tops the original Sonic games, 1 through 3.
The N64 has a lot of great 3d platformers and adventure games, but my personal favorite is Harvest Moon 64, if you've never played a Harvest Moon game, you should check it out.
The PlayStation was big on RPGs, and Final Fantasy 7 through 9 are all epic games. My favorite is Final Fantasy Tactics though.
I recently wrote a Top 5 list of video games I've played, and 3 of them were from the 90's. Check it out here: