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.