I find using old t-shirts (and dresses and soft pants) for crocheting fantastic: the material is free, you can see the results quickly (a bathroom rug was a bit too tedious for me) and the sky is the limit in what you can do.
On the right I have a few examples on what I’ve done. Pot coasters are great, as it is easy to get variation, I have e.g. made bunnies and chicks for the Easter table and frogs to a children’s party. Personalised baskets/ gift bags have also been a favorite of mine, the bottle bag in the picture was the first one I’ve tried to make.
Once again, I haven’t used any patterns but I got the first idea to make a basket out of old t-shirts from a Swedish women’s magazine called Hemmets. I have used a size 12 hook (not suitable for making kettle holders as the holes get too big for those).
Free But Fun 
Thanks for your tip, Quimper Hitty!
I have woven rag rugs using t-shirts as the raw material they are really colourful. If you cut a big spiral starting from the bottom hem of the shirt you get a very long string (t-shirts without side seams work the best). if you pull the string slightly the sides curl in. Actually the string is really useful for lots of things!