Depending on which Mac you have you may have three choices to upgrade to: 10.7 Lion, 10.8 Mavericks (both paid for upgrades) or 10.9 Mavericks (free). Upgrading to any one of them may render some of your older applications unusable as none of the upgrades support Rosetta which enabled older PowerPC apps to run, so it's worth checking for compatibility problems before upgrading:
http://roaringapps.com/apps?index=a
Also, before upgrading, make sure you have enough RAM for the new OS to run efficiently. They all state that 2gb is required, although 4gb or more would offer a much better user experience:
http://store.apple.com/us/product/D6106Z/A/os-x-lion
http://store.apple.com/us/product/D6377Z/A/os-x-mountain-lion
Mavericks is available directly from the Mac App Store in the Apple Menu.
Before upgrading ensure that you have tried and tested backup that you can restore from should you need to for any reason.