As website owners may know, sites with more high quality links pointing to them–that are from sites which themselves are ranked more highly by google–have higher listings in search results.
Website directories are sites whose listings are hand-picked and filtered by real people, as opposed to algorithms, so they are weighted as more trustworthy sources because they are expected to be good sites rather than sites that are designed to trick the search engines.
Wikipedia on web directories.
I compiled this list for myself and hope it comes in useful for others. Feel free to contact me if I am making any glaring omissions.

Below is a list of web directories specializing in art, roughly in order of pagerank by google:

• http://www.artnet.com/
• http://www.re-title.com/
• http://www.theartlist.com/
• http://www.artsearch.us/
• http://www.art-bridge.com/
• http://www.artpromote.com/
• http://www.yourartlinks.com/
• http://www.artquotes.net/
• http://worldartistregistry.com/
• http://www.123artist.com/

Surrealist Directories:

• http://www.surrealists.org/
• http://www.surrealism-artlinks.com/

General Directories:

• http://www.dmoz.com/

(Homepage has a higher pagerank than all the directories listed above.)

• http://dir.yahoo.com/