Is it the same in the Character palette? If not, can you find out which fonts they are (from looking into Windows>Fonts)?
Especially if yes to either, you may gave corrupted preferences. You may try to Ctrl/Cmd+ASlt/Option+Shift during startup of Illy, or Move the folder.
In the font preview menu some fonts show fine, others have blank space where their name should be (it's like illustrator is trying to generate a preview but can't). When I select those fonts and draw a textfield and type text not text shows. Like illustrator doesn't know how to show the font. Fonts are default ones, like Verdana. In other applications (e.g. indesign) they work just fine. Deleting pref folder didn't work.
Fixed it. I did a basic search for .lst files (fnt.lst) and deleted them all. That didn't work, but later I turned on 'all files including hidden'. Now it found lots more adobe fnt.lst files. Deleted them all and illustrator font preview list was fixed again.
Well done, flash. I had forgotten about that option.