I have OS X v10.6.8. I want to upgrade to Mountain Lion but it won't let me.

You can go directly to Mt Lion if your machine supports it, however if it doesn't and you want Lion you call Apple for the link.

FYI,

Your current PowerPC based software is NOT going to work if you upgrade to 10.7 or beyond.

So check first for your third party software, it may be a very expensive upgrade.

http://roaringapps.com/apps:table

10.7+ really requires 4GB+ of RAM (more if you use virtual machines) verses the 2GB minimal Apple says.

With a boot hard drive, you should copy all your users files to a external drive and then remove them from the internal boot drive before upgrading, this will have a effect of OS X upgrade being written the faster parts of the boot hard drive and avoid much of the "I've upgraded OS X and now my machine is slow" issues. You of course can return the files after the upgrade has finished.

Make sure the boot drive (regardless if HD or SSD) is not near completely full before upgrading.

Despite taking these precautions, if your machine is older or low performance, it might not run the later OS X versions well at all.

There is a risk of firmware/drivers bricking/causing issues, I don't recommend upgrading OS X on a machine that is out of AppleCare.

I lost a 4 year old perfectly fine (Snow, Windows and Linux) working 15" MacBook Pro due to the OS X Lion upgrade.