Tripod

• when a stable platform is required, especially when no camera or subject movement is occurring
• landscape photography
• long exposures
• macro and product photography
• situations where a remote trigger/tether is used

Monopod

• compromise when a tripod is to heavy/bulky to be carried (hiking, travelling)
• for supporting large lenses when the subject is moving (birds and animals, sports) - the monopod allows the camera to be panned as the subject moves more easily than a tripod
• also can be used when there is sufficient light outdoors, so that a tripod isn't really required, but a monopod can provide a little extra stability to prevent camera shake

Gorillapod - this has its uses in tabletop photography, with small cameras, or travelling when it can be carried in a purse or bag. Not really a true replacement for a normal tripod.

Length of legs - the main advantage of longer legs is that you can position the camera at the photographer's eye level, making it a lot more convenient to frame and focus. I would say this is especially true of a monopod as you will be looking through the viewfinder and don't want to be hunched over.

Longer legs may be an advantage in some situations.

On the other hand, for other shots it's useful to have a tripod that can position the camera very near to ground level. Apart from very small tripods and gorillapods, some tripods have legs that unlock and extend out almost perpendicular like so:

and others have reversible centre tubes so the camera can be mounted upside down.

If you get a tripod with longer legs, you'll want to be sure it's a sturdy tripod or it will be wobbly and defeat the purpose of having one in the first place.