I have many, many ripped tubes. Yeah, I know I could patch them, but I'm gonna be realistic and admit that I probably won't. Are they good for anything else? Once I used a couple of them to strap a large container to my back. But that's it. Is there a reason to save these?
Funny you ask this now. This weekend I saw a number of pieces of artwork all made of bike inner tubes. It was in Pilson at a neat shop called Concrete Age. They must know the artist as the work was displayed there. They are at 1932 S. Halsted, phone 312-226-3542. Maybe they can help you have your tubes turned into art!
If they are unrepairable, I like to cut them in half length wise and remove the valve half, thus leaving a half tube--still a full circle. With this, I place it, sometimes with disk glue by 3M, to the inside of the tire itself, then install the tube as normal.
I have a lot LESS flats from doing this and have never felt any extra weight or negatives. From time to time, I will replace tires and and pull out the half tube liner I usually find glass that never got to the inflated tube.
(this is for clinchers only; tubulars don't work as well)
Make a belt with the tubes. Get creative. Clothing and what not. I like the hand bag ideas. I saw new biker bags made by Bontrager made of tubes and what not. I think the handle bar wraps is awesome (totally gonna do this next), no more cork needed. Tie downs, suspenders (I would giggle if I saw this in public), shoe ties, wrap your whole bike in tubes for a scuff free surface, I like the idea of making a sling shot, wrap around young saplings to keep the rabbits from eating the bark, but art is the best use I have heard of yet!
Someone was telling me about chairs that were made from old rims for the frame and used tubes for the cris-cross webbing that you actually sit on. Similar to outdoor furniture (chairs and loungers) that you would find at the pool or the beach. I don't have a link or picture, but it sounded cool.
I've successfully repaired dozens of tubes that have been given to me by my cycling friends over the years. My reputation is such that people toss me punctured tubes from the trunks of their cars at ride meets. Usually the puncture is nothing more than a "snake bite" impact-type flat and easily repaired.
Tubes with blowouts, large holes and tears I can't repair. These I collect for recycling. REI sponsors a recycling program at the annual Chicago Winter Bike Swap. But I always keep JUST ONE old tube in the garage for DIY repair projects. I've cut them up and glued them on the bottom of chair legs, used them as makekshift gasgets and seals, and even used them to replace the rubber cushions on my Thule bike rack.