The easiest way I've seen to keep track is to tear off the endflap of each box of ammo. They don't take up much space and they let you know not only how much you've shot but also what kind of ammunition. That works well if you have just a few guns.
If you have a number of firearms, you can do something along the lines that I do. I have a spreadsheet that I use to keep round counts for each gun as well as rounds fired since last cleaning for the guns that don't get cleaned after every single range trip. I also use it to record ammunition that shoots well in a particular firearm and accuracy results. In addition, it's a good way to track modifications/maintenance done on each firearm.