Snow Leopard to Lion was a big change, and a lot of apps were incompatible (especially the old apps that required Rosetta). Lion to Mtn Lion is a smaller change under the hood. Haven't heard of too many apps not functioning.
It looks like Apple may be taking a similar approach to OSX as it has with the iPhone. Every 2 versions are a big release. Leopard and iPhone 4, Snow Leopard and iPhone 4s, Lion and iPhone 5, Mountain Lion and ???? -- we'll see.
That being said, a clean install and migration from Time Machine backup does have some benefits. It cleans out any cruft the old OS may have created and also serves as a defrag process. If you format the drive and install fresh, all of the block gaps you've developed over the years go away. OS X doesn't have a huge issue with degragmentation, but every little bit helps and this is a perfect time to take care of all the minor issues in one fell swoop!