Q: Can my PC run Windows 7?

The short answer is yes (probably).

If your PC is less than 5 years old then you should be fine.

The official minimum system requirements for Windows 7 are:

- 1 gigahertz (GHz) or faster 32-bit (x86) or 64-bit (x64) processor
- 1 gigabyte (GB) RAM (32-bit) or 2 GB RAM (64-bit)
- 16 GB available hard disk space (32-bit) or 20 GB (64-bit)
- DirectX 9 graphics device with WDDM 1.0 or higher driver

More: http://www.microsoft.com/windows/windows-7/get/system-requirements.aspx

If you're not sure what hardware is in your machine or you want a more detailed assessment then download and run the Windows 7 Upgrade Advisor (Beta)

The Windows 7 Upgrade Advisor is kind of like a stand alone version of WEI and will assess your PC's hardware checking the four main system requirements (CPU, RAM, HDD & Graphics) and give you a detailed report outlining whether or not your machine is capable of running Windows 7.

The Windows 7 Upgrade Advisor will also list any devices or programs you have installed that may have issues with Windows 7 and where possible provide info on how to address these.

More info: http://www.microsoft.com/windows/windows-7/get/upgrade-advisor.aspx

Of course, if your PC doesn't meet the minimum system requirements... this may not necessarily be the end of the road.