"Zoom" lenses are simply lenses that have an adjustable focal length; "prime" lenses, in distinction, have a fixed focal length. Many people mistakenly equate "zoom" with "telephoto zoom," but that's not the case -- there are wide angle and normal zooms as well. Zooms are very popular these days and most of you are probably using them, but as anything in life they have pluses and minuses and I'd like to inform you of some of the issues involved in choosing one type over the other.
Let me warn you at the outset that I am biased in favor of prime lenses. Let me also point out that I am photographically a fundamentalist and I don't wish my particular forms of kookiness on anyone else. Just because my personal style of photography is painstaking and deliberate, perfectly suited to prime lenses, doesn't mean that you should emulate my choices. Indeed, many if not most top pros use zooms. But my observations may give you information that will help you make an informed choice of what is right for you.
The most obvious advantage of a zoom lens is that one lens covers many focal lengths, replacing many prime lenses. You don't have to pay for or carry around the weight of the extra lenses, nor do you have to incur delays from changing lenses. Just twist or slide a collar, and instant focal length choice is yours. Moreover, you can precisely select any focal length at all that is within the range of the zoom, whereas with prime lenses you are stuck with only certain, fixed choices.
Modern zooms also often test on optical benches to be as sharp as prime lenses. Early zooms were optical disasters, but nowadays they can be of fine quality (although clunkers still exist).
So what's not to like? Let's start with that optical resolution. While the best zooms can test to be as sharp as prime lenses, my experience and that of many others is that they still don't offer images as "crisp" as those from prime lenses. What I believe is going on is that there are two things that go into making a picture look sharp: resolution -- what level of detail can be discerned, and contrast -- how well the brights and darks are preserved. A lens with great resolution but poor contrast will show detail, all right, but it will be all muddy and mid-toned. The resulting image is not pleasing, even though the resolution, technically, is there. It is my belief that zooms, which contain more optical elements than prime lenses, have enough internal light scattering from all those optical surfaces that their contrast suffers, and thus the resulting images lack "snap." In other words, there is more to judging a lens than resolution, and I think that prime lenses win over zooms in terms of overall image quality due to their better contrast. Those extra optical elements also make zooms more prone to flare.
Now, whether the (possibly minor) optical advantage of prime lenses is worth putting up with their inconvenience is a matter of personal taste. For my work, where I am trying to eke out the best possible image in sizeable enlargements, it's worth it, but most people are not in that boat.
There are other reasons why I don't like zooms that might or might not matter to you. A one-touch zoom is subject to "zoom creep" if the lens is pointed up or down: gravity slowly moves the zoom collar if the collar drag is not properly adjusted. Also maddening for me is that, for most (but not all) zooms, the f-stop changes as you zoom. I usually set my exposures manually, and if I have an exposure figured out and I decide to zoom, I have to make sure I adjust the exposure accordingly. I'm busy enough when I'm making images; that's more than I care to keep track of. In addition, the front element of some zooms rotates as the lens zooms, a disaster if you've got a polarizer or a split neutral density filter already adjusted the way you want it.
And there's more. The closest focus distance of zooms tends to be farther away than that of prime lenses. Zooms tend to have slower maximum apertures than prime lenses. I've never trusted my ability to maintain precise focus while zooming a one-touch zoom. And a lens shade, which you should always use to minimize flare, is problematic on a lens whose focal length is variable: except for a few fancy lenses that have an automatically variable lens shade built in, you are stuck using a shade appropriate for the widest possible angle of view and it won't be sufficient at the longer focal lengths.
My final reason for disliking zooms is quirky and personal. For me, all that flexibility that zooms offer, paradoxically, is too much. There are a lot of choices to be made when creating images, and I am one to fret over options. So I fare better if the process is simplified. I do best if I can simply say "this is a wide angle image," or "this requires my longest lens." I judge how I want space to feel in the image (which is a key effect of different focal lengths), opt for the appropriate lens, and get on with it. No fussing, no fretting, I just choose a lens and get on to the next decision. This approach is not without risk: I have lost images that required the precise cropping permitted by a zoom . . . but surprisingly rarely. For me, it works best if I stay with prime lenses.
So there you have it: reasons for and against zoom lenses, some quantifiable and some personal. Now you can make your own choice of what is right for you -- and that is the best lens to own.