Take it from someone who has ended up with too many globals before: the best way to do this if you have over, say, 25 levels, is to use a global dictionary object ("LevelProgress"). Then, just add keys ("Lvl1,Lvl2") and check for their state when needed.
This way, it's easy to manage non-linear progress too (like an Angry Birds game, where you might have beat level 7, but not necessarily beat level 5 or 6).