I played Gears 2 while only playing about 15 minutes of the first Gears, does that count?

I did it with Fallout 2, I wasn't a fan of apocalyptic scenarios, then I stumbled upon it, given with a gaming magazine, and I was amazed. But I didn't play the first chapter, after, the 2nd chapter plot and environment's vastness appealed me more and I don't like to play not following the time line (this cast of mind still prevents me from watching the "new-old" Star War saga chapters ).
I bought Quake II too having only played the first chapter's demo (and obviously QII itself's demo) before.
Oh, and Ecstatica II, found it already old in a bargain bin, by then the first was stone age and impossible to find.

...

Oh, yes, how could I forget it, Duke Nukem 3D

I don't remember others...

Edit:

Magic Carpet 2

Most games mentioned don't really require knowledge of the Sequel to understand the games story, with the exception of Tales Of Symphonia..maybe..

From what I've read, MGS3 is chronogically first.

No Final Fantasy is a sequel except X and X2.

Pikmin II wasn't really a sequel. Hl2 didn't require much backstory aswell.

I've played resistance 2 without playing rfom

Most of the time, I go back for the prequels. If the game is only available on PC, and then the sequel is available for consoles, or it the developer makes jumping in easy, I buy the newer version.

If they are linked by the story, no, I'd never play a game if I didn't play the prequel. f.i., I didn't play yakuza, but wanted to buy yakuza 2, so I looked all over the internet to get a copy of the first one before purshasing yakuza 2.

I played Dead or Alive 2 without playing 1 and Dead or Alive 4 without playing 3.

I played TES 4:Oblivion before the first 3.

I played Advance Wars 2: Black Hole Rising before the first.

I played GTA 3 before the first two.

I played Super Metroid before Metroid and Metroid 2.

I played Metroid Prime 3 before 2 but 1 first.

I'm sure there are more but I can't think of them at the moment.

I typically try to play the first game if story matters.

Metroid Prime 3, Fire Emblem 10, Resident Evil 4 all come to mind.

 Same here.

(>'.')>