My top 5!

The first four are in no particular order.

Super Mario Bros.
What can I say? This is possible the first video game I ever played. I can remember getting up during the night when I was a kid, and playing this, when I should have been sleeping.

The Legend of Zelda
Another of the first games I ever played, and I have loved the Zelda series ever since, they haven't changed all that much over the years, but they have never stopped being awesome.

The Legend of Zelda: The Ocarina of Time
This may have been the first N64 game I ever saw. I was amazed by the graphics and the game play, even though it was a while before I got to actually play it. Once I did, It quickly became one of my favorite games, I've beaten it so many times.

King's Field
I clearly remember this was the first PlayStation game I ever saw. A family friend had been playing it as I watched, it looked so interesting. I didn't actually play it until years later. It can be a very hard game, but can also be very rewarding when you finally take out it's many monsters, and discover it's varies secrets. I've loved the series since, and I really hope they make a 5th King's Field.

Earthbound
Here it is, my favorite game of all time. I remember seeing the very large box when we visited a rental store as a kid, my brother had heard about it, so we rented it. At first I didn't care for it, but as I played further, saw all the weird humor, and the battle system, and much more, I really started loving it.
It also still has the greatest players guide ever written.

Some of those might not be my favorite games, or my top five favorite(Other then Earthbound)but I think they helped shape me into the gamer I am today.