Depends on which model and when you bought it. If it's an iMac, you're good all the way back to mid-2007. Mac Pro needs to be early 2008 or later. Mac Mini needs to be early 2009 or later.
If it won't run Lion/Mountain Lion, it won't run Mavericks either, unfortunately.
Also note that some features (e.g., AirDrop) aren't available on older machines running Mountain Lion, even if the basic OS runs. I don't know if that's been changed for Mavericks.
My girlfriend uses a 2008 aluminum MB (non-Pro), and I never had any issues upgrading her to previous versions of OSX. Now it's running Mountain Lion and downloading Mavericks as I type.
