It's a complicated issue. While I am against sweatshops, the people who work there don't really have a choice as to where they work, and if their sweatshop was to go out of business they would probably be worse off than they already are, so for the time being, I don't go out of my way to not buy clothing made in sweatshops, but I am in favor of getting rid of them and establishing better places for those people to work.
I'm against horrible sweatshop conditions but I agree with the other poster that it's probably a singular source of income for many workers, so if you take down the sweatshops, a lot of people would be worse off.
American Apparel doesn't use oversea sweatshops. It's kind of their selling point, but they overcharge for basic clothing. Admittedly, the fabrics are nice quality. Still, my opinion of AA tends to be negative as it feels like they are overplaying the fact that they are sweatshop free.
I really don't want to wear clothes made in sweatshops, and I try to make sure what I buy isn't made in sweatshops. I'm willing to pay a few extra dollars to ensure that clothing is produced humanely. American Apparel doesn't use sweatshops.