Can't say that I have closest thing to a fire is when my V5500 started smoking

Had a psu fan bearing catch on fire once. That smelled great!

Only once and that was a long time ago, it was a board that shorted out somehow and the traces to the front panel went up in flames underneath the board but I managed to cut the power in time to save the rig. The board surprisingly survived after a quick fix 😲

I don't know if this counts, but my Athlon XP 2000+/Abit KT7A PC burned out back in November 2011. Powered it up, left the room to make breakfast, came back 15 minutes later to find the PC dead, room full of faint white smoke and the smell of barbecued electronics. PSU, memory, video, sound, HDD controller, NIC were also goners. Close examination revealed several popped caps around the CPU socket, VRM and memory slots and burn marks inside the Sparkle PSU. The smell didn't go away for over a year (had to use a lot of air fresheners), and is still faintly present in the wall area where the PC was closest to.

An old Maxtor 4GB hard drive also has a strong burn smell, yet nothing looks out of place - no burn marks, no bad or missing components. It still works, but the smell is so bad I have to keep it inside a box with foam padding. I'll probably send it to a recycling center eventually.

Almost. I was restoring my first PC. Short story: I was playing Commander Keen 1 when I smelled something toasting. I checked it and the AT connector on the motherboard was melting.
Long story (including a related mod, which turned out to doesn't be neccesary because the mother is malfunctioning): My first pc - restoring

I had an SCSI cable catch fire. The loose connector at the end went into some pins of my sound card. One of the wires in the cable got hot and the plastic just burned away. Fortunately I was there.

The sound card has been noisy ever since.

Time ago a Ide to Sata converter, powered by the fdd supply connector, shorted and melted psu rail wires.

Had a P4 system I was upgrading/swapping cards. Had the case open, inserted a USB stick to boot from, turned the machine on and instant smoke. Turned it off quickly but I saw it came from one of the IC's of the mainboard. A straight line on the IC, all melted/bubbly. Mainboard was completely dead after that.

Not me, but ~15+ years ago I was in a text chat with a friend who typed "FIRE" and disconnected.

He had a P3 ABit motherboard which had just died. It got replaced with the same model, which died again after the same length of time (not sure if that one qualified as "FIRE" or not).
The cheap capacitors problem was really bad with ABit back then so I wonder if that's what his problem was. They could have failed short and maybe he had a cheap PSU that didn't know when to shut off.

I had a monitor go up on me once... I used to live/work in Iraq and on one of the site locations the power quality was shit (generator) so power kept sagging / surging. We had UPS's of course but they were 16th hand or close to it so they were bypassing and not smoothing the supply as they should. In short, the monitor along with the rest of our electrical's was getting it hard... and decided to let us know giving a few flickers of flame on its top end and a plume of dark smoke. Fair to say we left the door open for a bit and punished the office for not fulfilling the latest of our many requests (a UPS!)

A relatively minor incident, a USB plug with an LED light in it (why? don't ask me..) started burning and smoking.
Neither the USB port nor the printer on the other end of the cable were damaged.

Maybe a bit off topic, but funny. Time ago my DVD ide player had problems reading a installation cd and without any reasons and sense it began to accelerate to a really scaring speed (!) until the cd inside literally exploded inside with a incredible boom sound!

I had an ancient PSU with probably bad caps light right the hell up as soon as I turned the system on. Good times.

This happened a few weeks ago, I got a IBM machine (5160 I think) plugged it in without checking the caps... POP and smoke.

I have seen a 30 to 60 cm flame, comming out of an ATX psu once. (not my computer)
And yes... Then there are those "dell-laptop catching fire" videos on youtube.

https://www.youtube.com/watch?v=pizFsY0yjss

Once one of those IDE->SATA power adapter cables caught fire in a PC at the University. Luckly it wasn't connected to an HDD, because the DVD drive's connector melted, but nothing else was affected (I saw the smoke pretty much instantly and pulled the power cord).

Never an outright fire, but I did come close a couple times. Once was back in the late 90s when an IC on an old Connor 250MB hard drive started smoking and glowing hot. I had been testing it in an old 486 system I had at the time, but rather than have it actually mounted inside the case it was just sitting loosely on the ledge of the case. It shifted slightly while running, shorting the controller board against the chassis.

The second time was in 2003 and wasn't quite as dramatic, but still resulted in some magic smoke being released. In a moment of stupidity, I tried to run a powered external USB hub off one of the PS/2 ports on my computer. Eh, it was an ECS motherboard, so nothing of value was lost. :p

I've had a few capacitors and flyback transformers go bang over the years but never an actual fire.

One of the more stupid things I've done was when I found an external dialup modem that needed 7VDC to run, so I thought it would be a clever idea to connect GND to +5V and VCC to +12V on my PC power supply, so I could supply it with seven volts without needing an extra wall-wart. I'd seen this trick used to slow down 12V fans so I thought it would work.

Well it did work, but what I hadn't factored into the equation was that the serial cable has a shield, and this is connected to GND at both ends. So because I'd put +5V onto the shield at the modem's end, I was shorting +5V to GND across the serial cable. The resistance was high enough that the PSU could cope with the load so the modem worked, but when I went to touch something I found the serial cable was very hot, and it only took me a moment to realise what I'd done and shut everything down.

Luckily everything survived that "experiment"...

Not my own system, but I was building (back in 2004) a server computer for my brother. High-end Athlon64, PCI-X Raid with the new SATA connectors with 4x36gb Raptors, etc. I was installing the floppy drive, and the power cable came out. I plugged it back in, then proceeded to turn on the system to "test" everything.

As soon as the power hit the floppy a massive POOOF of magic smoke blew out the front and back of the floppy drive, and the floppy power cord melted all the way back to the PSU. The damn cable was moved over one pin worth.

$3000 system almost went up in smoke. Luckily the only thing that died was the floppy drive and the cable. PSU still worked fine, sans one floppy power connector.