Archive your existing system and try it. Finding out will cost you all of $20. If you don't like it, restore from your backup.
Many 32 bit apps will not work. Rosetta is gone so PowerPC apps will not work. Your printers will probably need to be reinstalled. Nearly every third party system hack will break, often in ways that are not obvious. If you are using marginal third party RAM or your hard disk is about to fail, updrading OS X will reveal those flaws. Lion and ML are built around a trackpad interface with its countless gestures for navigation, so unless you purchase a MTP you are going to miss much of what makes Mountain Lion useful.
Like every major Mac OS release since the beginning of time, Mountain Lion likes memory. More is better. Consider 4 GB a practical minimum, and at least 8 GB to be comfortable.
Some people can't stand the Lions and think SL was Apple's pinnacle achievement. They will reply soon, extolling SL's virtues, if they haven't already spewed vitriol about ML while I'm typing this.
SL to ML is a big leap. Don't expect an effortless transition; expect to devote at least a week before you draw any conclusions about your long term relationship. I've used every Mac OS since 1985 and consider myself a Mac traditionalist, but I'd never want to go back to SL, not ever, for any reason... but to each his own.
I use both - separate partitions. I can run older games and programs not compatible with Mountain Lion. Most of the time I use Mountain Lion.
Check to make sure your applications are compatible. PowerPC applications are no longer supported as John pointed out.
You can also check by going to the menu, select About this Mac, click on More info…, then click System Report and select Software/Applications.
If you have applications that you want to use that aren’t compatible, you can retain Snow Leopard and create a new partition to install Mountain Lion on or you can run Snow Leopard server in a virtual mode.
If you can/do upgrade, I recommend you make a copy of the installer and move it out of your Applications folder. The installer self-destructs. The copy will keep you from having to download the installer again. You can make a bootable DVD/USB stick to install using this free program.
Thanks for the suggestions. I run a video editing suite, and rarely have more than a day or two between jobs to "mess around" with upgrading, so it's a scary proposition. My main reason to upgrade is that I just bought a MacBook Pro, and want the two to "talk" to each other, share calendars via iCloud, etc.
Maybe if I get a slow week, I will take the plunge!
Yes. Don't do it until you have at least some kind of break. Attempting an upgrade without enough time is a sure way to having problems.
The other thing is backup first.
I suggest that you create a bootable clone for backup. At least that way if things go sore, you can be back up and running againt with just a reboot.