Hell yes.
Far Cry 3 stands completely alone apart from 1 and 2. 2 is mostly standalone, though there's a theory that a character from 1 is in it. So yeah, you don't need to play 1 or even 2. Edit: the protagonist and location of each game are completely different if that wasn't clear.
I'd suggest giving 2 a try, though. It's a bit more raw and less hand-holdy than 3. The companion mechanics are surprising. When you "die" then a companion will (usually) appear to drag you away from the combat in a little scripted thing, then hand you a pistol and help you to your feet. I love games where failure isn't necessarily game over. Though the companions can die, if you leave them wounded on the ground.
Far Cry 3 makes you more of a superhuman. It's probably more fun overall, I have more hours clocked in it. It also has a decent story. A lot of the characters come off as insanely self-absorbed, but I think that's intentional. Far Cry 3 also has a separate 4-person co-op campaign with new characters, which I was shocked to discover after hundreds of hours in single-player. I haven't played much of the co-op but it seemed to have all the markings of a decent co-op experience.
I haven't played Far Cry 1. From what I've heard it's an extremely linear, extremely frustrating FPS. No open-world like 2 and 3.