I know you can minify PHP, but I'm wondering if there is any point. PHP is an interpreted language so will run a little slower than a compiled language. My question is: would clients see a visible speed improvement in page loads and such if I were to minify my PHP?
Also, is there a way to compile PHP or something similar?
PHP is compiled into bytecode, which is then interpreted on top of something resembling a VM. Many other scripting languages follow the same general process, including Perl and Ruby. It's not really a traditional interpreted language like, say, BASIC.
There would be no effective speed increase if you attempted to "minify" the source. You would get a major increase by using a bytecode cache like APC.
Facebook introduced a compiler named HipHop that transforms PHP source into C++ code. Rasmus Lerdorf, one of the big PHP guys did a presentation for Digg earlier this year that covers the performance improvements given by HipHop. In short, it's not too much faster than optimizing code and using a bytecode cache. HipHop is overkill for the majority of users.
Facebook also recently unveiled HHVM, a new virtual machine based on their work making HipHop. It's still rather new and it's not clear if it will provide a major performance boost to the general public.
Just to make sure it's stated expressly, please read that presentation in full. It points out numerous ways to benchmark and profile code and identify bottlenecks using tools like xdebug and xhprof, also from Facebook.