Top five most important? Personal favorite? Highest selling? Play/replayability?
For most important I'm not sure it's possible to limit to 5. More so if you are including all systems. #1 would have to be Pong. Without the first one there are no others. #2 would be Mario or perhaps Mario Cart. Mario because it was THE game to have, though I prefer Cart as it gave us a popular 4 way split screen/party game. #3 would be Goldeneye? The first to give us damage based on where you shoot? #4 would be Doom. First of the great FPS games. #5 would be Half Life? First to use the modern control setups. But notice this list doesn't include adventure, RTS, RPG, etc games. How can you have a top five that doesn't include Pitstop, Pole Position, Diablo, Star Craft/C&C, etc.
My personal favorite games of the "modern era" would be TF2, Diablo 2, Red Alert 2, Half Life, and Quake. Even though some of these are very old, I still get together with my friend and play them at our houses. Quake hurts our eyes, but we've played it for so long against each other we don't know how to stop. (Same with RA2.) The replay on these are awesome.