Since it's not production ready yet: no
Since it's not production ready yet: no
Q^3, which can render Quake 3 maps and will eventually be its own game: https://github.com/Jeaye/q3
Servo, an experimental web browser being written by Mozilla: https://github.com/mozilla/servo
That said, rust has been written in rust, and every commit is tested against our test suite on Linux, OS X, BSD, and Windows. So while the language itself may be changing, any code you write in it at a given point in time should work. It'll just take some (small) effort to keep that code in sync with the compiler.
So if you are able to handle that risk, we'd love to have you try it out. It'd really help us find the warts in the language/stdlib before we lock in 1.0.
If you want to rewrite your codebase on a quarterly to cope with the changes, that's up to you, but I wouldn't.
I'm waiting for 1.0 to really start writing code in it.