I'm not familiar with CCleaner but if there's one thing I KNOW it's that you should always back up the registry before modifying it in a major way. If you're running Windows XP or a more recent version then your computer probably has a program called System Restore that you can use to take a snapshot of the registry. Then if the changes made to the registry cause problems, you can revert to the snapshot of the registry from before you changed anything.
You should always take these precautions before modifying the registry, however if CCleaner is a professional-quality, trustworthy program then it is probably smart enough not to do anything that would harm your computer.
Edit: I just downloaded it and tried it out, it's actually a pretty nice little program. When you are ready to fix registry errors it should prompt you to back up your registry. Just say yes then go ahead and fix the registry errors, I used it and it worked fine. If something is wrong just find the registry backup file and if you double-click it you should get a prompt asking you if you want to add the information to the registry. Say yes and the registry will be restored.