I am running both 32 and 64 bit CentOS as web servers, application servers and file server. CentOS and Red Hat are derived from the same source code tree. I haven't seen any difference in stability between the 32 and 64 bit versions in a server environment. The only problem I had was the availability of a 64 bit RAID driver for a new model HP server. HP had it available but only on request because it hadn't been regression tested. That was almost two years ago and they now made that driver available for global download on their website.
The main services which I have running on 64 bit are Apache, PHP, MySQL, PostgreSQL, SOGo, Samba, Subversion and NTP.