Why do I need root privileges to umount a drive at the command line, but not in Nautilus? How to change that?

Nautilus doesn't unmount the device directly; it talks over DBus to a system daemon (udisks-daemon) and asks it to unmount.

The daemon checks if you're allowed to do that, by contacting another system daemon, PolicyKit.

PolicyKit uses the configuration defined in /usr/share/polkit-1/actions/org.freedesktop.udisks.policy (unless the local system administrator overrides it in /etc/polkit-1). That file tells PolicyKit that users with active console sessions can detatch drives, so PolicyKit talks to a third daemon, ConsoleKit, to see if you have active console sessions. Logging in via gdm counts as a console session; logging in via ssh doesn't.

There's a command-line tool udisks that lets you unmount devices without using sudo, using the same mechanism:

udisks --unmount /dev/sdb1

that unmounts the filesystem; I can also detatch the whole device with

udisks --detach /dev/sdb

which makes the LED on my USB key go dark.

The situation might have changed -- in current Ubuntu 10.04 umount works without sudo for USB drives. Generally I think that the command

gvfs-mount -u /media/the_device

(gvfs-mount is in the gvfs-bin package) should always work.

Current answers are deprecated. Try:

gio mount --unmount *mounted location*

get the current mounted partitions with for example:

lsblk | grep media