It's got nothing to do with the size of the lens. An ideal lens hood prevents extraneous light from entering the lens. Ideally any light rays that do not contribute to forming the image on the film should not be allowed to enter the lens, especially bright rays. Extraneous light rays create lens flare which will degrade the quality of the image. You should always use a lens hood.
What if the hood causes vignetting? My camera doesn't have come with the option of an original hood, thus my choices are left to the generic ones. One that I am considering is the Hoya 58mm rubber hood.
Regarding vignetting, it's easy to check especially if you are using a digicam. Just test out a shot or too with a small aperture and you can see if there's vignetting. Of course you may have to download the image to your PC to see the full frame though, cos I understand the LCD on the camera body may not show the full frame, but then you can always zoom in to the corners to have a look.
Once you have a hood, use it at all times, even at night, not just when you are shooting in bright sunlight. Like I mentioned above, any light that is not directly involved with creating your image should be kept out of your lens.