Depends on how the app was written but generally NO, heaven forbid. The Z uses Qtopia and apps must be written specifically for it, just as it would for a Palm, Mac or whatever the Microsoft effort is this week. ;-)
I notice this kinda question every week at least! I find it hard to believe that people are buying Linux PDAs and getting confused about what can run on it, obviously, someone, somewhere is not being clear enough.
I don't know i got a "z" cos i wanted the power of linux in my hand. if i'd have wanted a shitty palm or ppc i would have got one of them.seems a little inane> don't you agree Emperor.