How do I find the UUID of a filesystem

Look up data on /dev/sda1:

topher@crucible:~$ sudo blkid /dev/sda1
/dev/sda1: UUID="727cac18-044b-4504-87f1-a5aefa774bda" TYPE="ext3"

Show UUID data for all partitions:

topher@crucible:~$ sudo blkid
/dev/sda1: UUID="727cac18-044b-4504-87f1-a5aefa774bda" TYPE="ext3"
/dev/sdb: UUID="467c4aa9-963d-4467-8cd0-d58caaacaff4" TYPE="ext3"

Show UUID data for all partitions in easier to read format: (Note: in newer releases, blkid -L has a different meaning, and blkid -o list should be used instead)

topher@crucible:~$ sudo blkid -L
device     fs_type label    mount point    UUID
-------------------------------------------------------------------------------
/dev/sda1 ext3             /              727cac18-044b-4504-87f1-a5aefa774bda
/dev/sdc  ext3             /home          467c4aa9-963d-4467-8cd0-d58caaacaff4

Show just the UUID for /dev/sda1 and nothing else:

topher@crucible:~$ sudo blkid -s UUID -o value /dev/sda1
727cac18-044b-4504-87f1-a5aefa774bda