Running computers in basement storage room safely
3x 300 watt servers together would produce ~3070 BTU/hr. ~1023 BTU/hr each.

There's no particular hazard to running the servers near a water heater or furnace, other than the heat associated with those items raising the baseline before you add the heat thrown off by the servers. Most system administrators would choose not to but that's from a "hazard to the computer" point of view, not fire hazard - Nothing quite like having a water heater fail and spray your servers with hot water to ruin whatever service you were running on them.

You have provided no data on airflow or ventilation - it's certainly possible that the temperature may become excessive without some active ventilation and/or cooling. 

If the ceiling height is 8 feet, there's about 89 lbs of air in the room. The specific heat of air is 0.24 BTU/lb/degreeF (varies somewhat with temperature and pressure), so in the absence of airflow into or out of the room and with infinitely insulating walls/floor/ceiling, you'd be looking at ~140F temperature rise per hour. Might be a bit toasty for the servers, though it would save a bit on hot water bills. Real walls, floor, ceiling will bleed off some heat, but you still might have a problem without some active ventilation. During the heating season you may well be able to arrange the cold air return so that the servers get cooler air and contribute to heating the house - in warmer weather you'll want to dump heat somewhere else, though you could get some benefit by using a heat pump water heater (or just an add-on unit) to provide some (erratic, as you use hot water) cooling and make use of the heat from the servers.