I don't recommend turning the page file off - Applications still do look for it and get.... upset... if it's not there. Also, just because your computer has a 64 bit OS and 6GB of Memory doesn't mean that a given (32 bit) application knows how to use it all. These are generally programmed with a 2GB application space, since that is what XP/Vista 32 provide. So on an application level something may still be hitting the page file to swap data even though there is still more RAM available to be used.
So instead of turning it off, I recommend turning the page file down - I have mine at 512MB on 8GB of RAM.
It's not that the app doesn't run - Rather, if the app fills up the space it's programmed to use (2GB for many 32 bit apps), then it goes to the Page file to swap data in/out. If the page file is shut off, that can cause errors and crashes.
That is not how it works. The 2GB is all it can address (or 3 or 4GB depending on OS and largeaddressaware).
A page in that address space can be backed up by physical ram or the paging file, but this is not something the app does, it is all internal to Windows. An app never goes out to the paging file by itself. Sure, it can check if there is configured a paging file in the system, but it cannot address it by itself.
Some apps, like photoshop, can work with more than 2GB of data by copying data from its address space out to disk when necessary, to make space for new data. But this is some internal virtual memory management in the app and has nothing to do with Windows' paging file. In photoshop that is called the scratch disk.