I have to say that that is not my experience. All the
pen/thumb/flash/whatever you-prefer-to-call-them drives I've ever used
have been FAT formatted, that is true, but all nine of my USB hard
drives (a mix of Western Digital, Seagate and Iomega) were NTFS until I
started playing with them. Now, most of them are ext4, except for the
Seagate and one of the Iomegas, which I've left as NTFS as they contain
my videos and music, which I *might* want to use on a Windows box, someday.

The answer I would give to the OP is this: if you're happy formatting
hard drives under Linux and you're *absolutely* certain that this drive
will *never* need to be hooked up to a Windows box, then I would
recommend switching it to a native file system (ext3/4, Reiser,
whatever, your choice) as a native format will handle file and group
permissions correctly, unlike either FAT or NTFS. Otherwise, leave well
alone and just use the drive as supplied; whatever its format, Linux
will handle it.

If you do decide to switch, the easiest way to do it is, as already said
elsewhere, using gparted - make sure to set the volume label to
something sensible though, as otherwise the system will mount it under a
default name which probably won't be terribly helpful.