The short answer is yes. The minimum system requirements for upgrading to Windows 8 are pretty minimal: You just need a 1GHz processor, 1GB or memory (2GB if you're on a 64-bit system), at most 20GB of hard disk space (16 GB for 32-bit systems and 20 GB for 64-bit ones), and a graphics card capable of running DirectX 9. That's it.
(About's PC Support site has a quick guide for finding out if you have a 64-bit or 32-bit system.) Of course, the minimum system requirements are hardly ever the optimal system requirements, but I did find Windows 8 to be zippier than previous versions. With a clean install of Windows 8, Windows 8 appeared to take less than 20GB of space.
You'll need to meet the screen resolution requirements for some features, including Windows Store apps--an issue if you're on a netbook--but otherwise, the upgrade should go smoothly for you if you've been using a version of Windows launched in the last few years.
As a precaution, though, make sure you're aware of: