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.
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.
Best of the Web
Best of the Web is one of the oldest directories, having been around since 1994, and is highly regarded. Cost when last checked was $99 per year or a one-time fee of $299.
Gimpsy have been around for quite a while and have had a good reputation and seem to have maintained their PageRank when other directories have lost theirs. Three levels of submission from free (long queue) to $49.
JoeAnt another long time player with a good reputation. Submission costs $39.99
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.