I would have to say Megaman.  I remember renting Megaman 1 when it first came out.  When I first started playing it I really liked its style it had.  It was a new platform at the time I was really digging it.  As soon as I heard Megaman 2 was released I went ahead and got it and from then on out I became a big fan of it.

That was the first gaming series I became a big fan of.

Hmmm It would be FF or Sonic but I don't know it anymore.

I liked the FF game on my NES but I was not a fan of it then.

I was a fan of FF when I played FFIII and I became a fan of Sonic when I played Sonic 2.

I really don't know anymore which of the two I was first fan of X_X.

Zelda. And it wasn't until Ocarina of Time. I hadn't looked at games as a series whole before that.

Mario.. I got my 64 along with it. Got addicted to it lol :)

when i was 11 (i think) a played Halo CE, i liked halo ever sence

As odd as it sounds, Kirby. I really loved that little pink puffball. From the GB game, to the NES, then finally Superstar on the SNES, I was constantly looking forward to Kirby games. I was sad that there wasn't a new Kirby for the GC, and I lost interest during that era, but I really loved Canvas Curse for the DS. Now Superstar Saga is being remade on DS with extra levels and a new 3D Kirby (akin to the N64 one) is being made for the Wii.

Civilization.

The first civ still stands as one of my favourite all time games.

Probably Mario. I started with SMB1/2/3 on the NES, then got SM64 on N64 launch day. Been loving the little plumber ever since. :P

After that, probably Kirby with Kirby's Adventure, then LoZ with Ocarina of Time, then Age of Empires with AoE2.

I'm pretty sure it was Sonic. It was far from the first franchise that I bought into but it was the first one where I would save up money in anticipation of a release.