Not quite, this is how it works. OS X is the 10th OS (the X means 10). Each time apple brings out a new OS they add 1 to the first decimal place, 10.0 -> 10.1 ->10.2 and so on, we are on 10.4 (codename Tiger) at the moment. The next one is 10.5 Leopard. I think each new one comes out roughly every 14 months.
What you do get for free are the upgrades for (things like bug fixes, patches, and sometimes extra features here and there) your *current* OS. We are currently on 10.4.6, the next update (which is 10.4.7) is due to come out very soon.
Apple also update their other programs, such as the ones in the iLife suite, click on the apple menu at the top left and select software update, if you haven't done this yet then you will have some updates to install!
By the way, if you are a student then you can get a discount on a lot of apple stuff including Leopard when it comes out (which will either be just before the end of the year, or just after).
