I was originally going to say "I always play campaign first" but... it depends on the game.
Now, normally, I won't buy a game unless I'm thoroughly intrigued by a central game mechanic or something along those lines. Except, of course, when the case is that I'm already a fan of the series. If either of those are the case, I play the campaign first, no questions asked.
However, there have been two notable exceptions: Halo 2 and MW2. I bought halo 2 because I had friends who played it all the time, I didn't play the campaign for a very long time. In MW2's case, I bought it purely for the multiplayer, and I still haven't even considered touching the offline game.