Great question!
Depends on the hobby I suppose.
Scrapbooking definitely costs me money. I use my scrapbooking supplies to make greeting cards though, and that saves me the money of buying cards which are ridiculously expensive.
Reading doesn't cost me anything other than gas money if I use the library, which I do a lot anyway. My library also has a "friends of the library" section where you can buy "once read" paperbacks that people have donated for $1. They often have the newest bestsellers on that rack, I'd rather pay $1 than around $8 at the store. I return the book to the library once I'm done so they can resell it.
Sewing saves me money on clothes for my family (mostly my girls) as well as other sewing for household decor... making doll clothes for gifts and just for fun for my girls, etc.
General crafting.. well... I make a lot of gifts so that definitely saves me money too (and I love creating these goodies, very relaxing for me!) I have a scrollsaw and cut out a lot of "country style" items, paint them and give them away as gifts, especially over Christmas time. Last Christmas was the first time I did this and I was really surprised at how great they came out. I can buy one plank of pine for around $5 and make numerous items out of that one piece. Real cutesy pieces that are great for decorating your house for Christmas... pieces that would cost around $14 to $20 to buy something similar at Wal*Mart, so I definitely saved there. Even factoring in the cost of paint it still works out cheaper, especially since I already have a lot of the paints anyway. My hubby bought me a belt disk sander for Christmas last year and this has saved me a lot of time on sanding the pieces
My SIL was horrified that he bought me a sander for Christmas, LOL! I'd rather have that than another diamond ring though!
Baking (hey, it's a hobby too, right?!) Definitely saves me money. Kitchen goodies are more things I give away as Christmas and other time gifts, especially my chocolate chip cookies that everyone loves and looks forward to.
The biggest saving anyone can get from their hobbies? Better health! It reduces your stress level which makes you less susceptible to succumbing to an illness.