A response center (or centre, if you're British) is the room or suite where a pair or trio of agents lives and receives missions.
Response centers in general are made of Generic Surface, and contain a console. Most of them are about the size of a dorm room and may or may not contain a storage closet and a bathroom—newer RCs are more likely to. Any other furnishings are up to the agents that inhabit them, and indeed many agents have been known to completely remodel their response centers. Mission souvenirs are a common type of decoration for response center walls, including body parts from Cute Animal Friends and Suvian artifacts. Response centers also commonly house minis or other pets adopted by the resident agents.
Even if present, the use of beds, chairs, cushions, and other items for reclining are often avoided in response centers, since it is common knowledge that as soon as one gets comfortable in one, the console will beep. This can't always be true, however, or they would go insane much faster than they do currently due to lack of sleep (and even in HQ the sleep deprivation would, eventually, kill them).
Some agents began using a TARDIS instead of a response center after the 2008 Macrovirus Epidemic, but once the quarantine ended, most people went back to their RCs. Currently, the only TARDISes in use belong to Time Lord agents.
Many locations in HQ are converted from response centers. DIA Central, for example, started life as a collection of RCs; one relic of this is its prison, which uses modified RCs as cells for offending agents. The Coffee Lounge, too, began life as a response center.
Response centers may have any number at all, regardless of whether it is a positive integer or even a real number. Jay and Acacia's RC did not have a number, but rather the letter F. It is unique in this regard. Other response centers may have letters in them, but they can't be a letter alone.
The most current list of response centers and who inhabits them can be found here.