I had the same problem when I upgraded to Tiger. Text in Camino (a Mozilla-based browser) would frequently overlap, making some words nearly unreadable. Upon firing up Font Book, I noticed many of my font families had a bullet ( • ) beside them, indicating that duplicate font files were being loaded. By expanding the disclosure triangle beside affected families, I could see which individual fonts were duplicate. I selected the duplicates and chose Edit > Disable Fonts (File > Remove Fonts would be another option), and then restarted Camino. Lo and behold, text rendered very nicely again.

In my case, the duplicate fonts were .ttf (eg. Helvectica.ttf) files that I had manually placed in my ~/Library/Fonts directory some time ago. They never caused problems in Panther, but seem to conflict with their corresponding .dfont (eg. Helvetica.dfont) files in Tiger.

I ended up having to do this, too.

Also, plain old rm of the files does not end up solving the problem - they get copied back again. I had to disable my user fonts from the Font Book application, then go and resolve all the duplicates as you mentioned.