Yeah, most software will run, but you can't say for sure. What specific programs are you worried about?
Many games will run, but won't run very WELL. A lot of that has more to do with hardware than software; for example, my old copy of Warcraft II is pretty much unplayable on any modern machine, because they're all too fast! You try to scroll an inch, and it practically shoots straight to the edge of the world because the scrolling is so much faster than it was supposed to be.
Other old games work perfectly, though. For example, I recently replayed The Legend of Kyrandia in OS 9 (both natively and in Classic mode, for testing), and it ran perfectly.