If you're young, you most likely don't have to worry about it. If you're older, it's a crap shoot. Some people swear by products but it's really genetics, age, and TIME!
If you lose weight quickly, you'll probably get some noticeable loose skin, but over time (about two years) it should firm up about as much as it's going to. If you lose weight more slowly, your skin has a little more time to catch up as your weight goes down. Either way, at the end of the day you can always build some muscle to "fill in" your arms bit. Though I'd recommend that anyway because who doesn't want arm muscles?