DMoz (also known as the Open Directory Project)
DMoz is one of the largest and best known directories and is one that is run on a volunteer basis. Google pays a lot of attention to it - so much so that they duplicate its content in the Google Directory. Being listed in DMoz can be of great benefit to your rankings in the major search engines but unfortunately there is a very large backlog of sites waiting to be assessed because many of the categories don't currently have editors.
Yahoo Directory
The Yahoo Directory is a pay-for-inclusion directory which was at one time essential to be in if you wanted good search results in competitive areas. A yearly fee is payable which when last checked was around $299. It no longer seems to be as important for natural search results but the directory itself is well used and you may find it worthwhile for that reason alone.
Looksmart
Looksmart was previously an important directory in the UK as they had a relationship with the major telecomms company BT, but since this ended they have declined in importance.