In GNOME, gvfs does not require root for mounting remote filesystem (ftp or ssh) and gnome-mount also does not need root for mounting external storage (usb drive, CD/DVD, etc).
Most systems probably would not want to have the whole GNOME just for some remote mounting, then you can use lufs, sshfs or ftpfs.
gvfs, lufs, sshfs, and ftpfs uses FUSE to allow non-root users to mount virtual filesystem; and unlike mount's -o user, FUSE do not require the sysadmin to arrange specific mounts. As long as you have the privilege for the mount directory and to whatever resources that are needed to construct the filesystem, you can create FUSE mount.
Why does mount require root privileges?
Because mount is primarily/originally intended for local filesystem, which almost always involves a hardware.
