If you want to keep the shirt as a shirt, you could cover the logo with some paper and do some bleaching designs. Just make sure to get bleach over the stains. If you're not crazy about a bleached shirt, you could do the same treatment and turn it into a bag
I reckon making little plush toys would be a cute way to make them into gifts. :) I also found another Pintrest board. I was looking for something to do with mine for a while, but I hit on something that works for me quite specifically--I have a long-haired, long-eared dog and need something to hold his ears away from his food if he's eating something not-dry. I made this little dino-snood for him, and I want to make a bunch of different ones when I have time.
Get the book "Drawing on the Right Side of the Brain" by Betty Edwards. It will teach you to draw. It's really incredible how it happens. I think they have a whole separate workbook now too, but I just read the original book and did exercises from it.
I can't imagine anything being as concise and effective as that book.
Addendum: If you're not comfortable with drawing strangers, feel free to use the wonders of modern technology (google images and youtube, "sports photography" and "ballet" are some of my favorite searches). You may lose some of the immediacy of quick sketching, but it'll allow you to build up a foundation.
And definitely check out "Drawing on the Right Side of the Brain". These are some other really useful posts if you're too broke for books.
Some of these are so flippin cool O_O This rug thing might end up as the fate for some of my T's that are too beat up and ugly to upcycle otherwise. And the jersey-yarn idea is great too...
I was going to suggest t shirt tote bags, which are especially quick and easy, and a neat way to display any designs you particularly like.