1 - I don't even know the name of the game or the system exactly. I was 7 or 8 and spending the night at my buddies place. It resembled a Colicovision but was called a something 'home computer'. It definitely started me down the path.
2 - Wasteland! Thats right the predecessor to Fallout was one of the first RPGs I ever played and also one of the most polished and epic(five 5 1/4" floppies).
3 - Super Mario Brothers. Probably in just about every ones list if they are over the age of 20. As far as I can remember one of my first run ins with a platformer. First and best.
4 - Doom. Brought things in to, as I knew it at the time, 3D for the first time. It all seemed so amazing and new and really kicked off what is now considered the standard. 3D.
5 - Half-Life. Not that it was the first online multiplayer game or even the first multiplayer shooter but it had the largest impact. For years it dominated LAN parties and I spent countless hours playing online multiplayer. Subconsciously I think I still hold multiplayer to the standard.
Just shy of these are the likes of X-Wing, Kings Quest, Tetris, Alone In the Dark, Netstorm and some others that I can picture and remember but don't recall the names.