If it's a mounted filesystem, you can use df -hT:
$ df -hT
Filesystem Type Size Used Avail Use% Mounted on
/dev/sda1 ext4 5.5G 3.0G 2.3G 58% /
none devtmpfs 229M 252K 229M 1% /dev
none tmpfs 233M 0 233M 0% /dev/shm
none tmpfs 233M 100K 233M 1% /var/run
none tmpfs 233M 0 233M 0% /var/lock
none tmpfs 233M 0 233M 0% /lib/init/rw
The "type" column indicates the filesystem in use; the "filesystem" column is the partition/device where it's located. (This example is from an Ubuntu Lucid system; my Debian system displays the root partition filetype as rootfs instead of the correct ext3.)
If the filesystem is not mounted, or df displays it as type rootfs, you can use a tool such as blkid, which checks the device more directly:
$ sudo blkid /path/to/filesystem/device
/dev/sda1: UUID="xxxxxxxx-xxxx-xxxx-xxxx-xxxxxxxxxxxx" TYPE="ext4"