Fix #1: Turn off your camera
This one usually works to correct most malfunctions. Simply turn your camera off, and then turn it back on again. If you camera still isn't working, move on to fix number two.
Fix #2: Take out the battery
Sometimes simply taking out the battery and putting it back in will get things back to normal. You might even try swapping in a fresh battery if this doesn't work.
Fix #3: Take off your lens
If something interferes with communication between the camera and the lens (the lens isn't mounted 100% correctly, or there's some dust in between the contacts), this can cause the camera to seize up. Try taking the lens off, and then putting it back on again. If this doesn't work, try a different lens, just in case it is the lens (and not the camera) which is malfunctioning. Another thing to try is to turn off your autofocus. In certain shooting modes, if your camera can't lock focus, the shutter won't fire. If working in low light or contrasted backlight, your autofocus might have problems locking on. In such situations, switch to manual focus and you should be good to go.
Fix #4: Unplug your electronic remote shutter
Unfortunately, your electronic remote is your camera's Achilles Heel, the point most likely to fail. If nothing else seems to work, try unplugging the remote. More often than not, a faulty remote is the culprit when your camera wigs out (especially if you are using a cheap off-brand remote). Problems with the remote usually manifest in one of two ways: either the camera seizes up, or the shutter starts firing continuously. Just having the plug in at an odd angle can cause problems, and simply taking it out and putting it back in (correctly this time) will get you up and running. A wet remote can cause problems too, but should be okay again once it has had a chance to dry. If the remote is failing, unplug it and switch over to the camera's self timer to eliminate vibrations after you manually trigger the shutter.
Fix #5: Take off your lens cap
Okay, I'd be kidding if I didn't see this so often. I've actually had workshop clients ask me why everything looks so dark through their viewfinder. We've all had those moments when we forget to do something basic and obvious, like leaving the lens cap on or forgetting to turn the camera on. When all else fails, go back to the basics and make sure you haven't simply made a rookie mistake!
"Hanging Out"—Spider monkey, Osa Peninsula, Costa Rica. The Osa is world famous for its epic diversity of wildlife. Canon 5DIII, Canon EF 200-400mm f/4L IS USM Lens with Internal 1.4x Extender, ISO 3200, f/5.6, 1/200 second.