Actaully because of the nature of open source applications ("I can build one of those!"), giving you a one for one replacement for your OSX apps is difficult. As you can see from the other answers for this questions there are at least a couple different applications for each type of app you're looking for.
Since there are so many different variations of text editors, music players, movie makers, desktop enviroments, the easiest thing to do would be to find a set of applications that you personally like and enjoy using. If you find that you're a Gnome desktop user, we a thing for some KDE applications and the occasional fling with Vim, no one is going to stop you.
Since you spoke of Ubuntu, I would suggest that you just go through their application library and start downloading applications that sound fun, exciting or might be usefull for you. Installing and uninstalling applications is trivial with Linux. Play with the thousands of applications out there and have fun.
Good luck and hope this helps some.