Based on Mike_Noren's description, I was pretty sure it was spirogyra, so I did some searching and found the following photo of someone else's tank and was able to confirm it because it looks exactly like the algae in my tank:

http://1.bp.blogspot.com/_dLGw_s0RLUw/R0XWtKpNGiI/AAAAAAAABAw ...

Thanks, everyone! I'm glad to hear that the algae is indicative of good water quality. I'm going to try the bamboo stick removal method. I think that will be less disruptive to the fish than me putting my hand in there to reef out bunches of algae every few days!

Does anyone know of a type of catfish that will eat thread algae? I have a recurring problem with it in my tank.