Pro - it helps cut down on lens flares from sources of light (like the sun)
Pro - it really helps you not to accidentally hit the front glass of the lens into things - in that way its a fantastic protection. Its very easy when shooting to be looking through the viewfinder and moving close and closer to something only for your hood to hit something in the way (a twig, bars, a pole).
Pro - it makes the lens look bigger and longer
Con - with some wide angle lenses you can get shadowing in the corners of the shot if the hood is fitted
Con - some macro lenses cannot shoot with the hood due to the short working distances.
in short always have you hood on if you can - its a great protection against things hitting your front glass
The pros:
-They can block extraneous light that might have caused flare or a loss of contrast.
-A solid hood can prevent objects from hitting the front element, keeping it cleaner and maybe preventing damage.
-They can make you look more 'professional'
Cons:
-They can make it hard to adjust a filter like a circular polarizer.
The reason the lens designers make lens hoods removable is for compact storage, filter adjustment, etc... It's not because they considered it optional to use. All of the lens designing and testing was done with the lens hood on, and they expect the lens to be used with the hood on.
Lens hoods are like seat belts. Most of the time it may not matter much to your driving whether you are wearing one or not. It's there for the problem situations. With photography some of those problems (flat contrast, desaturated color, flaring) may not be evident until you see a larger version of the photograph.
Some folks say it's too much of a pain to use lens hoods. C'mon, it's a pretty simple habit to learn; my hands do it automatically when I pick up the camera.