Note that this error only occurs on Leland servers, since the retirement of pubsw.
If you get an error like this when running any drush command:
php: error while loading shared libraries: libmysqlclient.so.15: cannot open shared object file: No such file or directory
Take a look at your ~/.cshrc file. In it, you will see a few lines like the following:
if ( ! $?site_path ) then set site_path=( \ /usr/local/bin /usr/sweet/bin /usr/bin \ /usr/pubsw/bin /bin /usr/sbin /sbin /usr/proc/bin \
etc...
If /usr/bin is either missing or after /usr/pubsw/bin, you'll want to fix that, then logout and log back in.
(Thanks marco!)
Alternative Method
Running the following command will update your .cshrc file for you:
updaterc
Note that the updaterc command will rename your existing .cshrc file to .cshrc.old.
(Thanks Sharon!)