A server room is important for a physical security standpoint. It's a good Idea to keep access to servers, backup tapes etc. secure from theft or malicious activity. Also climate control of temperature and humidity can be better controlled within a server room if the servers are not contained in a climate controlled enclosure. Also having the servers in a separate room can enable you to incorporate an alternative fire prevention system than what you may have in the rest of the building. For example Halon alternatives such as FM-200, Co2, FE-13 or INERGEN can extinguish a fire without damage to electronic equipment. (Halon is being phased out). I'm no expert on fire prevention, but non damaging prevention solutions are often overlooked. A sprinkler system or a corrosive agent can ruin 10's or 100's of thousands of dollars of equipment.
And the last thing I find important about having a server room is that it's nice to be able to shut the damn door sometimes and get some work done !