Many people use gift bags that are typically reused by the receiver(s) until they are no longer presentable. I like to use a canvas bag or other tote bag as part of the gift. You can also use newspaper and other large pieces of paper as wrapping paper: recent brides should hang on to aisle runner -- it's great!
You could use brown paper bags that you got while at the grocery store. You could also use newspaper, especially the cartoon section. You could also use colored tissue paper that you got in a gift from someone else. You could also use old vintage tins or boxes that are pretty and original.
Use recycled paper -- any paper you have around the house. I especially like to use the comic pages, but you can use plain office paper too. Decorate the paper any way you want to personalize the gift. Just remember not to use paper that has anything private on it.
My favourite alternative to regular wrapping paper is furoshiki, which is the Japanese art of wrapping things in cloth. It fits most objects better, needs no tape, looks prettier, and the cloth is reusable.