I'm a bit of both, really - and I think everyone is, to some extent! Listening and talking are essential to communication, and it's hard to get through life if you only do one or the other.
I often get friends coming to me with their problems, so I must be something of a good listener. If I sense that someone needs to talk, I'll encourage them, and let them know I'm there to listen (even if they just want to vent or rant).
However, if I've got a problem of my own, I'll only share it if I think the other person can help, or if it's important for them to know in order to understand why I'm acting in a certain way.
I won't put a mopey status on Facebook about it, because if I share something with someone, it's not because I want sympathy.
If I'm comfortable around the people I'm with, I'll talk a lot, but if I don't know them very well, I'm often quieter.
When I'm getting to know someone, I'm more of a listener - I think this is because I'm quite selective about who I'm friends with, and listening to someone is a good way to find out what they're like.
Talking + Listening = Communicating
I don't think it's possible to be either a 'listener' or a 'talker' alone. Both speaking and listening are essential parts of communication, and good communication involves knowing when it's best to talk, and when it's best to listen!