Can you enchant your other characters' gear?

Yes, you can. Before Wrath of the Lich King was released, the only way to enchant someone else's gear was to have them place it in a trade window -- which meant you couldn't use an enchanter alt to put enchantments on your main character's gear, and selling enchantments involved advertising in trade chat and meeting people face-to-face. (The horror!)

WotLK (via the Inscription profession) added enchanting vellum, which an enchanter can place an enchantment on to "store" it for later use. You can then send it to your alt or even list it on the auction house. To use it you just right click it like you would a scroll, then click on the gear you want to enchant.