Now I can attach my Android Motorola Atrix to my handlebars to view things like GPS and accelerometer data while I ride, and it didn't cost me a dime to make:
It's attached using 2 elastic straps tied in knots, but if I had a 2nd case to spare, I would permanently attach this one using zipties. I also used plain old shoelaces for 40km before I switched to the elastic straps, they both hold the phone on just fine, but the elastic holds it a little tighter.
There is virtually no wobble whatsoever. Even looking at my 3 axis accelerometer data, when riding on a smooth road, there is almost no wobble to even measure, and definitely none that I can see. When I want to lock my bike up to go in a store, I just take the phone out of the case.
To make it, I just drilled 4 holes, 2 for each strap to be threaded in and out of the case. I also wrapped black duct tape around the part of the handlebar that I tie the straps to, to add friction to prevent them from sliding around on bare metal (although that was never a problem before I added the duct tape). Because the case is silicone, it stretches easily to allow the straps inside the case and the phone still fits in it very snugly. I also cut two slits between each set of holes to make it easier to thread the straps through, but I wouldn't recommend it, because those slits might turn into tears.
Again, if you don't have elastic straps kicking around, you can use pretty much anything that's strong enough. I used crappy old shoelaces for a few days. After a day of hard riding, going over huge bumps and such, the phone is sitting just as tight as it was when I started. And after several days of riding, the silicone case is showing no signs of wear, or any sign that the holes I drilled might turn into tears.
Just wanted to show it off, what do you think?