1. Many manufacturers recommend it. When I first used bumGenius, I remember reading in their wash instructions that you could put their diapers through the dryer on medium with no issues. Later, they changed their recommendations to "line-dry covers and diaper shells. Tumble dry inserts, fitteds and prefolds" (bumGenius- http://www.bumgenius.com/help.php). Line drying actually saves your diapers and gives them a slightly longer life. This is especially true for the aplix on diapers. The less the aplix goes through the dryer, the longer it lasts.
2. The sun helps remove stubborn stains. I talked about this one in more detail yesterday, but again, the sun helps bleach out stains. It's especially effective on EBF poop.
3. The fresh air helps clear out stubborn diaper stink. After several dries in my dryer, my inserts often smell funky. One easy cure for that is to hang them outside. They smell great after a few hours in the fresh air!
4. It saves you money. It's no surprise to anyone that running the dryer costs you money. Even hanging just your diaper load saves you the money from running the dryer that one time. And since we all wash diapers regularly, that adds up to a lot by the end of the diapering days.
So the next time the sun's out, try hanging those diapers outside! Otherwise, you can always hang them indoors on a drying rack or you can do what I do and hang them on hangers on the shower curtain rod. :) Oh, and FYI, I don't have that awful border up in my bathroom anymore! Lol. We moved into this house with that and I've finally redone it! ;)