In a perfect world, your PSP would run on oxygen. Unfortunately, your PSP requires a battery for you to get your game on. Here at PSP Batteries, we've got what you need, and we've got them for cheap.
Official Sony PSP Batteries:

These are the only official PSP batteries manufactured by Sony. Although there are third party manufacturers of PSP batteries, these are the only three types that come directly from Sony and therefore they are generally believed to be the safest and most reliable for use with your PSP device.
Sony Slim "standard" Li-ion 1200 mAh: For use with your Sony PSP Slim and Lite device (2000 series) as well as the PSP-3000.
Sony "standard" Li-ion 1800 mAh: The standard battery for the original PSP Core Pack device (PSP-1000, aka PSP "Fat").
Sony PSP-280 2200mAh: Made to provide extended battery life for both the PSP Slim as well as the PSP "fat". However, due to its larger size, an extended battery cover is required to properly use this battery with the PSP Slim.
PSP Go Battery
The PSP Go is the latest Sony PSP device, scheduled for North American release on October 1st, 2009. This will be the first PSP device to feature a non-replaceable, non-removable rechargeable battery. The PSP Go will be 56% smaller than the original PSP-1000.
Third-Party Manufacturers
If you can't find an official PSP battery for your device or if you're looking for a better deal, you might want to check out some of the batteries made by third-party manufacturers. Although they generally aren't believed to last as long as the official batteries, they are often considerably cheaper. However, you should note that using batteries not officially endorsed by Sony may void the warranty of your device. Check the warranty documentation that came with your PSP device for details.
Click here to browse deals on PSP batteries made by third-party manufacturers.