People who do fiber projects are often split up into two groups: process* and project. Process people are motivated by the process of doing the craft. Project people are focused on having something completed in the end. I'm definitely a process person. I've got a big bag of completed hand knit socks that have been pretty much ignored since I finished them that proves it.
Weaving is a process that I enjoy. I have an Ashford Knitter's loom that I got a couple of years ago. Once I get it set up to go, I can happily zip through yards and yards of leftover sock yarn. I then have a piece of handwoven fabric that I do not know what to do with. It goes to live with the hand knit socks and the loom gathers dust.
My other loom is a vintage Weave-It that my grandma gave me. It makes 4" squares. The process of making the squares is fun, but again, I don't know what to do with them. A few years ago, I saw ads for a company called Buxton Brook Looms. They were making looms just like the Weave-Its that were called Weavettes. I haunted their website for a while, hoping that something would appear in the pattern section. Nothing did, so I forgot about them until today. I don't know if Buxton Brook Looms is still out there or not because the link I found for them didn't work. I did find Hazel Rose Looms. They offer looms similar to Weave-Its, only they are made from wood.
My other finding was that there are a number of patterns on the web for things using little hand-held looms. The next time I start to burn out on a knitting project, maybe I'll give them a try.
*My wanderings during NaBloPoMo turned up a third category: pre-process. The pre-process knitter loves to gather together all the supplies for a project. Guess who has a big stack of specially made project bags, a big sock yarn stash, and duplicates of most sock-sized dpns? Paula, the Pre-process knitter.