EDIT: Yes, Influential on you, games that introduced you to new things or that you just really loved.
#1: Rayman: Mom had this on the PS1 and was the first game I picked up and played ever. Origins is the only other Rayman game that can stand up to the original.
#2: Super Mario Land 2: 6 Golden Coins: Got this along with my Game Boy Color. First game that was truly mine. Spent hours replaying this amazing game.
#3: Wario Land 4: I remember going to the store a few months after the GBA launched and picking out this game since you could be Wario, the final boss of Mario land 2. This is one the greatest platformers ever made IMO and it's just weird and creepy.
#4: Pokemon Ruby: The game that got me into Pokemon, Parents later found Red and Silver for me too.
#5: Halo 3: Not the best Halo game, but I made a lot of new friends at school becuase everyone was looking for people to play with after this came out.