It's separation anxiety. It will come and go a few times over the first few years of your baby's life. Then kindergarten will start, and before you know it your kid will be headed off to hang with friends and not looking back and you'll be the one wishing you could cling. Ride it out, but know that it's just a phase.
Definitely this. The worst thing you can do is give in. I have a girlfriend whose son is a monster at drop of time because she caves instead of walking away. He's almost three now, and as much as I adore him, he is a BIG whiner. So not attractive to the three year old girls in the room.