If you use an ancient PS/2 keyboard, try jumping into Windows' Device Manager, uninstalling the appropriate PS/2 keyboard driver, and restarting your PC. It's also possible (but unlikely) that, somehow, your PS/2 ports got shut down via your motherboard BIOS.
For USB keyboard users, one easy trick worth trying is to switch the USB port you use for the connection. Shut down your system and move your keyboard's USB connector from the front of your case to one of the motherboard's USB ports, or vice versa. If you're using a USB 3.0 port, try switching to USB 2.0. In some instances, a keyboard with any USB 3.0 ports needs to have a USB 3.0 driver installed in order to work properly. If you have a ton of other USB devices plugged in to your system, see if unplugging a few of them improves the keyboard situation.
And, of course, if you're rocking a super-fancy game-centric keyboard, try uninstalling and reinstalling the drivers for your device.
My Computer Is Trapped in a Cycle of Continual Reboots, With Constant Blue Screens
When your computer becomes trapped in perma-boot land, we recommend thinking back to what you were doing immediately before you started experiencing the problem. Were you installing a new piece of hardware? A new driver? A new application?
If you can boot into Safe Mode (press F8 after your motherboard posts), do so and then attempt to reverse whatever you did just prior to your computer's freakout: Uninstall the new application; remove the new driver; or scan your system for malware (you never know). If you have Windows' built-in system restore feature enabled, you can roll your PC back to an earlier system restore point in an attempt to return it to normalcy.
If you have no idea what you might have done to upset your system, you have to decide whether to try to fix Windows with various random tricks (reinstalling drivers, uninstalling dubious applications, running chkdsk, and so on) or whether to spend your time in safe mode copying your mission-critical files to a separate drive. Once you're done, format your troublesome primary drive, reinstall Windows, and copy your files back to the drive.
If you can't get into safe mode before encountering a blue screen, you might want to pop your hard drive out of your desktop, replace it with a new hard drive, reinstall Windows to the blank drive, and then copy your critical files off of your old drive after-the-fact. If you still run into repeated BSODs even with a brand-new drive installed, you have an unknown hardware issue--perhaps memory, perhaps overheating--and it's time to roll up your shirt sleeves and get creative (or to head for the PC repair shop).
Something's Burning--My System Is Emitting a Strange and Unexpected Odor)