I haven't played Gears of War 1 or 2. Because of the great marketing hype created for Gears 3, I was thinking of buying one. How will my gaming experience be if I directly jump on to Gears 3?
If you only play multiplayer, then you aren't missing anything by skipping Gears 1 or 2 (other than familiarity with the game mechanics).
As for the single player, there is a story and it does tie up a lot of loose ends from the first two games (I haven't played much of the campaign yet, this is just what I've heard from reviews and such). There is a "previously on Gears" intro movie that you can play before the campaign starts to get you up to speed.
If you watch the intro movie, and possibly read about the plot of the first two games on the internet, you would probably have enough info to not be confused by the story in Gears 3.