Phew! Im glad someone agrees with my (admittedly conservative with a small "c") viewpoint on this subject.
Speaking as a senior Bioinf/sysadmong at a University I would expect such a decision to go to various levels of tender and meeting with consultation from internal and external experts. However to cut to the chase we went with Horde IMP for the web frontend. We also recently moved from a UWIMAP backend to a Courier backend with little in the way of problems. With sufficient clustering/reduncancy we've had little in the way of system downtime except in cases where it was inevitable (such as city-wide power outages). I'd recommend Squirrelmail for SMEs/ smallish organisations where you want to get something solid and straightforward up and running quickly, and Horde if you want more configurability and functionality. At the end of the day though it all depends on how your mail backend is set up, and migrating that to a new system is probably going to be more of a headache than migrating to a brand new web front-end for your mail service.
EDIT: P.S. I would class migrating form pop3 to imap/*spit*exchange*spit* to be more of a priority than your web front-end. For DPA/ IP/ convenience having mailboxes centrally stored is far more agreeable than direct pop3 downloads