A user once showed up at the office door, and claimed that the "printer smelled funny". That is never a good sign. What had happened was that they had loaded iron-on t-shirt paper into a laserwriter. The paper, or rather its coating, had in turn melted around the fusor, the most expensive replaceable part. No actual fire, but it did smell pretty bad.
Fire is rare in server rooms, or rather "significant heat incidents" as one might see in the official reports. There may not actually have been a fire despite all sorts of burn damage from the, I don't know, electrical arcs.
Water damage is more common; one might find a nice pond in the server room and incipient mold carpet in the hall one morning. Or maybe there's a raised floor; the floor is covered with a rat's nest of live 20 and 30 amp power lines, and you have to drag up heavy floor tiles to get there, and hopefully not stumble in as you try to get the water out. There used to be one computer in that room, so it had been repurposed over the decades. One water leak ended up going into the fan path of a chiller; this lead to a nice spray of water over the firewall rack. The technician was nice enough to install a modification so future leaks would not spray water into the fan path. Why that fix had not been done at the factory was maybe a good question.
Very expensive printers have also shipped with plastic bits in the paper path. This caused jams, oddly enough. A similar conversation was then had with a different support tech. But no fire...