Windows Vista, Windows 7, and Windows 8 all come with a system performance measurement, Windows Experience Index, that tells you how well the computer will run Windows. Beyond that overall score, however, you can access more detailed information for other components of your system using the baked-in WinSAT (Windows System Assessment Tool).
You'll find the Windows Experience Index score under the Control Panel > Performance Information and Tools (or by searching for "experience index"). That number starts from a low of 1 to a high of 5.9 for Vista, 7.9 for Windows 7 and 9.9 for Windows 8. The higher the score, the more powerful your system is. The lowest-rated component in your system determines your rating; in my case, I got a 5.7 (on Win7) thanks to the integrated graphics on the laptop.
You can get a lot more information, though, than that overall score. As Chad Schultz points out on his Microsoft TechNet blog, the WinSAT tool benchmarks more hardware components: CPU, disk, graphics, memory, and so on.
Head to the folder %SystemRoot%\Performance\WinSAT\DataStore to find XML files on those components. Open one up and you can find individual scores.
This is a quick way to get a read on your system's performance, without having to download anything. If you're going computer shopping, you can also check the Windows Experience Index and WinSAT to see how capable a prospective system is.