UPDATE: The info in this post is deprecated. See the new post about eAccelerator instead.
I installed Turck MMCache PHP accelerator and I got a big improvement.
ApacheBench reported 4.52 pages per second before and 12.47 pages after installation (a Wordpress 1.5.2 page on a 1.2Ghz PIII). That a 275% increase in performance, with currently no observed problems. I tested this with both Apache2 and lighttpd, and got a similar boost with both.