If I installa the new operative system do I loose programs I installed before?

Question

Just a question: I installed Photoshop Elements on Snow Leopard and I wanted to upgrade my MacBookPro to Mountain Lion. If I install this upgrade, do I have to rebuy Photoshop or does it remain on my Pc?

Answer 1

Basically, you won't lose them, but you may lose other important files and folders that they need to function (preferences files, mostly), so I were you, I'd back up my Home directory (the one bearing your username), and the Applications folder, on a backup support of some sort, and copy their content (not the similarly named folders you've backed up) back on your startup volume after installing ML.
You should also note that some important preferences files are stored at the root of the system, and not in your Home directory. Those are the files related to startup items and launch daemons for system-wide (as opposed to per-user) applications. I'm pretty sure that most Adobe applications store some files and kexts there, probably under /Library/Adobe or /Library/Application Support.
Those preferences files will be recreated by their parent application upon first use, but you'll lose the settings you had saved prior to the ML install if you don't back them up too.