I concur with the above points about her being clingy and possessive etc. I think in a realistic and positive way of dealing with it however (as someone who used to be quite paranoid - actually no, I still am quite paranoid), there's ways to deal with this reassuringly.
You could reinforce (and stand firm about it too) that you want to hang out with your mates and you should do. The thing I had a problem with when I kinda used to do this was all I wanted was reassurance - if my boyfriend at the time had told me even the day before he was planning something that would have been awesome, but naaaah, he always left it until 5 minutes before whether or not he'd arranged something and it's kinda like this feeling of 'being let down'. I say just give her a heads up - not so much that she's like your mum and you have to tell her where you're going, just say "by the way, I'm hanging out with the guys/my mates on Friday, I'm really psyched, haven't seen them in ages"
You have to pull this off with complete confidence - if she starts to falter, then be like, well why are you so freaked out about it? Is she worried you're going to run off with someone? If so, why not arrange a group thing, introduce her to everyone, let her get to make up a real judgement of someone without immediately jumping to 'all his girl mates are trying to get with him'. Give her a chance to be a friend to your friends - not all the time, but to get to know them, your friends deserve to have the respect by your girlfriend and vice versa.
Anyway, these are the only realistic things I can think of - like a lot of other people have said, if you're calling her obsessive, clingy, paranoid and it's annoying you and basically, you're dissing her, are you really sure this is a girl you want to be with?
I'm not saying to treat her like some special case, but if you want to make this work you have to manipulate the way she is manipulating you (into leaving your friends). Make her realise your friends are awesome. TOTALLY AWESOME. And that you need some of your own space.