They looks cool even in the spreadsheet...

Guess I'll add my experience to this page - seems like everyone has a slightly different solution to this problem, and I had to spend a lot of frustrating time getting OpenOffice to a usable state. I tried all of the suggestions above, as well as some from other sites, and followed the instructions on this page:
http://corefonts.sourceforge.net/
After all this, my fonts in OpenOffice still looked horrible. I finally changed the depth of my display to 24 bit from 16 bit. That finally fixed it for me. Fonts not only look perfect in writer and calc, but they generally look better in all applications as well.

For anyone ending up here looking for information on this issue the OO Font Troubleshooting Guide

http://www.openoffice.org/FAQs/fontguide.html

is a good source. In particular it notes that font rendering is handled differently on 24 and 32 bit depth displays.

Antialiasing for drawing objects is finally ready in OpenOffice.org 3.1. Also, it draws text using Cairo now, so antialiasing fonts should be easy (though I haven't noticed problems in years).

Maybe because this thread is over FIVE years old?