Squirrelmail scales quite well to large multi-user environments. It is used by one of the largest ISPs in the Netherlands as their default webmail system. The main problem I see with it is the lack of development. They are in the 1.4 series now for several years, and the development of the promising 1.5 version with a more graphical GUI seems to be stopped. The good thing is that maintenance and security fixes for the 1.4 series are still available. I use Squirrelmail as the de facto webmail software on my systems. It works, but especially the HTML-mode viewer is not impressive. Also messages with HTML embedded in the main message don't display very well.
I have recently done a few installations with OpengroupWare (OGo) and Scalable OpengroupWare (SOGo). The functionality is impressive but it is a significant amount of work to get it working. OGo is a groupware application which offers also document management, task planning etc. SOGo is simpler in its functionality and focuses mainly on email, but it has a more appealing user interface than OGo and scales easily to several thousand users.