I am excited to see that rubber based crossbows are now covered here as well. I have worked with "slingshot style" weapons a lot these past few years, built everything from micro slingshots all the way up to car sized slingshot cannons. I dare say that I have amassed quite some experiences with Charles Goodyear's ingenious invention.
Therefore, I thought I elaborate a bit on the issue of rubber as an alternative energy source, compared to wood, steel or compounds.
Cheap. You can make a powerful crossbow band set for under five dollars.
Available. You can use gymnastics bands, spear gun rubber, even surgical tubing.
Easy. You don't need expensive tools or skills to make a crossbow with rubber. No comparison to making a crossbow with steel or wood as energy source.
Powerful. Rubber can be stretched far. About 5,5 times the relaxed length is usually achievable. This gives you a loooong power stroke, much longer than wood, steel or compounds would allow. This means you can achieve very high energy levels without much draw weight. The longer acceleration phase does that for you. A 45 lbs slingshot crossbow can achieve as much energy as a commercial high end 175 lbs model, if the tiller is long enough.
Narrow prods. All you need is enough clearance for the projectile and the bands. Rubber based crossbows can be very compact.
Easy "cable" change. Since rubber is usually not pre-stretched, exchanging the bands can be done in seconds, without any tools.
Vulnerable. Rubber is a natural material, and will break at some point. You can get thousands of shots from a single bandset, but if you max out the performance, you may only see 50 shots before you got to repair the bands.
Must be kept relaxed. Rubber looses power quickly in drawn out condition, so you should not cock a slingshot crossbow and then wait a long time before you shoot. Now this can be compensated by using heavy rubber, and also the rubber "heals" quickly (full force is back after 15 minutes if you relax the bands again), but this issue is serious for hunters.
Long tillers are called for. The downside of the stretchiness is that you need a long acceleration. An easy slingshot crossbow can be very narrow, but is usually long, musket style I'd say. Now this can be compensated by bullpup constructions and rollers to remove the dead play, but a simple, straight forwards slingshot crossbow is a long thing.
Cams don't work. Cams can dramatically increase the manageable draw, so compound crossbows are much easier to cock. The let-off effect eases the draw in fully cocked condition, which eases the pressure on the lock/trigger mechanism. But this does not work for rubber, as the "slippage" effect is dramatic. The bands will stretch very much between the "pouch" and the cams, making the cams useless. You can use rollers (= pulleys) to reduce the dead play in the bands, making the weapon more compact, but what you don't get is the "compound" effect.
Uncertain legal situation for hunting. While in many countries (most of Europe anyway), hunting with any kind of crossbow is illegal, there are many countries where you can hunt with one. But often there is a minimum draw weight. Here we run into the problem that a slingshot crossbow is more effective than a conventional one,so the minimum "legal" draw is complete overkill for a rubber based model.
Temperature sensitiveness. Rubber works best when it's hot, and does not work well in freezing weather. Not a problem, your slingshot crossbow will still pack a punch even in winter, but you need to adjust your sightings every time before you start the day.
Reputation. Yes, people may chuckle, even crack jokes, when you show up with a rubber based weapon and declare that it is serious. The jokes disappear quickly when the shooting starts, though.
No commercials models available. That's right, if you want one, bring out that old toolbox and start woodworking!
Is this list complete? Certainly not. I just compiled it from the top of my head. If you want to add something, please post away!
Greetings from late summertime Germany