Photographers are bombarded with all kinds of accessories that retailers try to sell us (UV filter, anyone?). I am personally on a very tight budget and I don't like purchasing things that are frivolous, not to mention that I avoid lugging gear that doesn't help me make better pictures. I thought I might break down the use of lens hood and explain what they do and if using a lens hood is really necessary.
The primary function of a lens hood is to help block off-axis light from entering your lens. This will reduce the effect of flare. Flare shows up in your images in two ways. The first type of flare is what I call 'starburst' flare, where a spot of color or light shows up in your image. Second is 'fade' flare. 'Fade' flare shows up as a general loss of contrast and color. If you are taking pictures out in sunshine and catch the light at just the wrong angle, your picture suddenly looks milky with a severe loss of contrast. Everything looks flat and dull; this is 'fade' flare.
A secondary function of a lens hood is to provide some protection to the front element of your lens. In some situations where a camera is either dropped or swung carelessly, a lens hood can be large enough to protect from a direct impact into the front element.
This picture is showing some 'starburst' flare because of the position of the sun in the frame.
In most situations, I think it is beneficial to use a lens hood, and it is an accessory that I recommend purchasing if your lens did not come with one. There isn't much of a downside to using a lens hood other than adding bulk to your lens. Off-axis light can be a problem in bright outdoor conditions as well as indoors with overhead lights. Certainly, if the light source is seen in your final image (like the sun shining in the corner of your picture), you will still be prone to flare and a hood can't do anything about this. However, for all other sources of light that fall outside your image frame, a hood will help to block this unwanted light.
Again, I love to save money where I can, but in this case I suggest purchasing the lens hood that is designed for your specific lens and matches the lens manufacturer. The shape needs to be exactly correct; otherwise, it can actually show in the edges of your pictures. I purchased the EW-83J lens hood for use with my Canon 17-55 f IS. It currently cost around $40. Sure, it would be great if Canon shipped this hood with the very expensive lens, but since they don't, just suck it up and buy the hood. It is well made and has proven quite durable. The inside surface is covered with a flat black, very tight textured felt material that helps to reduce reflections from light hitting the inside surface of the hood.
The end result of using a lens hood is achieving higher image quality by reducing off-axis light. In short, your pictures will have greater color depth and contrast and you will have the added side benefit of gaining some protection for the front element of your lens.
I have only come across one, and it has nothing to do with image quality. I don't feel that having the lens hood attached ever reduces image quality, but it does have one drawback. Camera lenses are often large to begin with, and adding a hood makes them even larger. When taking portraits, especially when the working distance is close, the combination of large lens/camera and hood can become intimidating to your subjects. If I'm shooting people indoors, where the risk of flare is usually very low, I will often take the hood off so that I am a bit less imposing on my subjects.
EDIT: I have forgotten one other situation where you should avoid using a lens hood, and that is when you are also using a built-in flash. The large hood can often block the light from the built-in flash and make a shadow at the bottom of your picture. I didn't think of this right away as I so seldom use the onboard flash and instead use off-camera strobes.