udisks2 is the package that (among many other things) is responsible for automatically mounting removable media under
/media. Well, not directly under
/media - it creates on-the-fly a new subdirectory with the volume label (or uuid, or serial number, depending on the mounted filesystem type) and then mounts the removable media in that subdirectory.
Starting with Fedora 17, udisks2-1.94, the mount path has changed from
/var/run/media/<username>, where username represents the currently logged in user. If you use the command line a lot (like I do), it's not very convenient to type all these path components (even with autocompletion). Perhaps the reason behind this change was to avoid mount point conflicts (and permission problems for filesystems that don't support UNIX permissions) between multiple logged in users. But I doubt that two (or more) different users can mount the same volume in two different places at the same time.
I created a small patch against udisks-1.94 that reverts the mount location to
/media. The patch is trivial, it just disables the code block that calculates the path in
/var/run. Fallback to the old
/media location was already implemented.