The Depo is one of the most effective birth controls on the market, but has some side effects that put women off. (I'd never personally use it. I went with a non-hormonal IUD) Side effects you might get are odd spotting, heavy/lighter than normal periods and over time no period, weight gain (this is a real common one) headaches, breast tenderness and a few other I can't think of. You can google for a proper list of side effects and the number of women who experience them.
I took one depo shot back in september. I gained 10 lbs almost immediately. My appetite just tripled. I will NOT be getting another shot and will look for another form of birth control. When I was looking into getting it I heard from a lot of women that they really disliked it. I also had a couple of women who said they actually got pregnant on Depo. The only reason I got the shot was to try and help boost my milk supply after giving birth. I won't do it again.
But like Clysta said, look at the depo website and see the complete list of side effects.
I had unprotected sex while on the depo and didn't get pregnant but both my mother and sister both got pregnant on it!
It all depends on the person but I agree look at the site.