I recently bought a Logitech Performance Mouse MX and am very happy with it. It is wireless and uses a single standard rechargeable AA battery. However it has two characteristics that make it interesting. First off, it comes with an Eneloop LSD AA battery, which is nice because it makes it similar to a built in battery except that in a few years I can just replace the battery trivially. Second, it can recharge the AA battery while inside the mouse. It charges via micro USB either from the computer or from a provided power adapter. What is very nice is that the mouse still works while charging. Which means that even if I run it completely dead I can just either toss in a different AA or plug it into the computer and have it recharge as I use it.
The only problem is that it retails for about $80, which is rather absurd for a mouse. However, if you keep your eyes open you can get it cheaper. I got mine for http://slickdeals.net/forums/showthread.php?t=2170526" shipped after rebate.