Previous posters are correct...
While some applications install by simply unpacking an archive, the majority go through the installer framework, which means registering their presence and post-install config (as required) in the "Registry". This means that while you can copy the application binaries to your USB drive (i.e. copy+paste the folder containing the application), this won't copy over the registry information which can frequently provide essential startup, config, key info that the app wants.
Some apps, like games, look in the registry to find out what cd/dvd install device was used, then go and try and read from that device to verify the install/play media is still there - this is particularly annoying when you clone the install media and mount it on a virtual cd/dvd because it then has the wrong device path...(roll up sleeves and grub around in registry time - again)
On some occasions (like when I'm backing up an old, soon to be destroyed and replaced laptop) I'll copy the application and take a dump of the registry. With the exception of checks against physical install media, this usually works well enough for me - although I little manual intervention is required to restore and normalize whatever registry info is needed.
Of course, by now you're probably thinking "meh, I can't be bothered with all this hassle".