Its fine to be jealous, and its fine to angry at guys who make a move on your girlfriend. I've been on both sides of that coin, and yeah it's totally justified.
Yes, you should talk to your GF, and tell her what you think, and that you're unhappy about this guy. However, she may either no believe you, or be unwilling to confront him, and that means you may need to do the job yourself.
Even if you trust your partner to tell them where to go (as you do yours, and indeed i do mine) that doesn't mean he's not a dick and deserves to be put in his place. I am DEFINITELY not beyond taking a swing at (and on occasion beating the crap out of, or one notable time throwing through a garden fence) people who go too far, and won't stop.
I mean, my girlfriend is pretty damn hot, and has many interesting and attractive qualities, and yes I feel very lucky to have her. I don't go round harming anyone who lusts after her, because it'd take a lot of time, and for the most part they know that they haven't a hope in hell of it going anywhere and all they do is treat her nice and compliment her various artistic endeavors. That's fine by me.
However, when someone is making a point of getting alone time with her (regardless of how genuine their affections may be) buying her stuff and generally getting over-familiar, then its time he and I meet, have a discussion, and he learn that backing the fuck off is what is going to happen.
Don't listen to anyone who says you shouldn't be pissed off. You should ABSOLUTELY not feel bad for feeling how you do. You should also ignore anyone who thinks that somehow it'll all end up alright if you GF just brushes him off. Unless she can stamp on him so hard he'll never speak to her again, it will just not end there. Plenty of guys (and at one time I was one of them) do this kinda stuff specifically to make themselves feel big and awesome and the manliest guy out there, and as that seems to be this guys deal.
In that case, this isn't about your relationship with your GF, its about someone pissing in your pocket and telling you its raining. Its the principal of the thing that matters, and you absolutely should not tolerate someone trying to cop off with your partner, even if she wouldn't ever do it. It's absolutely the trying that matters. Its just not cool. It directly equates to someone trying to steal from you. It doesn't matter that the doors are all locked and the alarm is set, the fact they are trying to means you gotta do something.
Have a full and frank exchange of words with him. Tell him in no uncertain terms to back the fuck off. If you can take him, then do so in private, then if he's a dick... well... you might have to make an issue of it. If not, do so somewhere public, and make sure either your GF is with you, or you have a couple of friends who have your back. If the former, its a good bet he won't try anything in front of her, if the latter, then you should be alright.
I am definitively not a violent guy, and under the vast majority of circumstances, I'd do anything to avoid situations where its a possibility. Chances are it won't go that far anyway. However, if words (then followed by cruder words, then shouted crude words) don't work and your GF is either unaware of whats up or is unwilling to kick him to the curb, then don't be squeemish of doing the job yourself.
Fear of confrontation is why guys get away with this crap. You wouldn't let someone just walk out of your house with your xbox because you didn't want to tell them to stop. Obviously its not directly the same, but if he's anything like I used to be, she hasn't even noticed whats going on, and that means it up to you.
For some reason we've gotten to that point of (and indeed the majority of this thread is) gasps of horror at the thought of confronting someone. Jealousy is something we've been programed to say is wrong, and it is, but only when its unfounded.
Man up, and sort the situation out. It is just not enough to say to yourself he's a douche, so meh. He wants to take your girlfriend from you. Don't let him even try.
No matter how much you trust her, or how solid and loyal her character is, love is a really fickle thing and particularly when someone appears to be open and honest and interesting and just awesome, it only takes a few tiny cracks for things to start imploding. Maybe you have a row or she has a few too many drinks or she just felt she could open up to him... What I'm saying is that its WAY easier than you think to make someone fall in love with you (not in lasting forever after way, just a little infatuation) if you want to. And while a lot of people are immune or too good to fall for this, its only takes a brief loss of control or perspective. There are lots of ways relationships can end, and this is one that will mess you up if it happens.