Hi all,
I just came across this same problem with a fresh install of MySQL and Apache, and I think I found the solution.
I had installed MySQL first, and I checked the box for the installer to add [server_dir]\mysql\bin to the system PATH. Then when I installed PHP, I manually added [server_dir]\php to my path so that when Apache loaded PHP, it could find the DLLs needed by the various modules.
When PHP tries to load php_mysql and php_mysqli, it looks for libmysql.dll, which exists in both \mysql\bin and \php. If the \mysql\bin entry comes first in your PATH, then PHP will try to load \mysql\bin\libmysql.dll rather than \php\libmysql.dll. However, since these are very likely to be different versions, this load will probably fail since php_mysql.dll is linked against the version of libmysql.dll included with theh PHP installation, and not the one included with an arbitrary version of MySQL.
Long story short, just make sure your PHP directory comes before your MySQL directory in the system-wide PATH, and that should fix the problem.