Twilight from the Twilight and Thebes Show called in with this question.
Wow. So in some informal instances it appears that it is OK to use thru; but I think I'd be remiss if I actually told you to go ahead and use it. My impression is that using the spelling t-h-r-u is kind of equivalent to dotting your i's with little hearts: people will know what you mean, but they'll think you aren't a very serious person. I would definitely stick with the more formal and widely accepted spelling: t-h-r-o-u-g-h.
Many people are surprised to learn that finding a word in the dictionary doesn't automatically mean that word is widely accepted by society. You'll find the words thru (t-h-r-u), irregardless, and ain't in many dictionaries, but that doesn't mean you should use them in your cover letters. It just means they are in wide enough use that dictionary makers believe the words must be acknowledged and defined.
There are just a couple of instances I could think of where it might be acceptable to use thru (t-h-r-u). One is in a text message to a friend because, like it or not, the expectations for grammar and spelling in text messages between friends are lower than in other forms of writing. Also, people are probably more likely to accept the informal spelling in places where space is extremely tight, such as on road signs, advertisements, or again, in text messaging.