Oh my goodness, hobbies...
1. Foraging- looking for free wild edibles by the side of the road/in forests. I bought my wild edible book at a library sale for 10 cents.
2. Taking free classes online- Busuu (languages) or Khan Academy (math/science).
3. Sewing- buy a cheap machine, or a used one on Craigslist. Find used tools (seam ripper, etc) at garage sales. I hardly ever buy new fabric- this makes sewing EXPENSIVE so I wait until I can find free fabric. Sometimes I get free clothing from my sister or other people. "Part out" the clothes and save zippers, buttons, and other reusables. Not only do you get free zippers, but you learn how the clothes are put together and how the pattern pieces should look. A sleeve or pant leg looks WAY different layed out flat than it does on a pair of pants. This leads to pattern design and fitting skills... extremely valuable.
4. Selling stuff on Ebay or Amazon.
5. Take stuff apart. Like old computers, pianos, anything free that is just going to end up in the garbage anyway. It's a great way to learn how things are made or how to fix things. I love music so I pick up cheap ones at garage sales with the sole intention of taking them apart and fixing them. You can also mix numbers 4 & 5, parting things out and selling them on Ebay. I took apart a doll (expensive name-brand one) with the intention of fixing it. I never did put it back together, but did sell the parts separately for more than the doll was worth new.
6. Cooking. This, like sewing, can be very costly, but not if you blend it with #1.
7. Writing/blogging. I've learned a ton about internet and code and all that, just by keeping a free blog.
Learning is the best free hobby I think. You become somewhat of an expert in many areas, and get the opportunity to help a lot of people, for free or paid work.