Well what would be the point of a short-term relationship other than "for teh lolz"? At least there's much more of a companionship element in a long-term relationship, because a true friend/lover will not abandon you unless you deserve to be abandoned or he/she is dying.
Emotional and physical affection and companionship don't need to last forever to be helpful, meaningful, and fufilling.
How does one deal with trust and worrying?
a) Say my girlfriend has done something stupid that hurt me pretty bad, and I ended up finding out myself rather than by her telling me. She apologizes profusely for it, is honestly sorry, and realizes what she did and how it's messed up the relationship. I know she won't do it again, and I know for a fact that she does truly care about only me and has no feelings for anybody else, but the fact is that it still hurts and I just don't know how to get over it - I can't she how she even did it in the first place (I think this is partially due to the fact that I've never done anything along those lines - never really even considered it - and so the idea of it is just completely strange and unnatural).
All you can really do is wait it out. Since she's sorry, won't do it again, didn't mean to, and you're obviously not broken up with her, so... that's about it. Give yourself some time.
b) As for worrying, is there anyway to stop worrying so much when she goes out with friends or things like that? I honestly don't know if it's just me caring for her that much (I honestly feel that I'm in love or close to it with her, though I haven't said it yet and don't plan to until I'm sure) or if I'm just paranoid - most likely a bit of both. I don't know her friends personally, but I do know that some of them are people that I honestly don't like her hanging out with.
Blah.
Everyone worries about those they care about, and it's perfectly okay to do so as long as you don't act irrationally on them. Are you worried because you don't trust she'll be safe or because of something else? Ways to deal with it differ based on this.