Almost all cameras have zoom lenses these days. There are exceptions: the Fuji X100s has a fixed 35mm equivalent lens. And of course, "prime" lenses (lenses which have a fixed focal length) are valued by many photographers for their clarity and great bokeh.
For many photographers, zooms provide a lens kit in a single barrel. "Kit lens" zooms in the range 18 - 55mm are often sold with consumer-level SLRs, and prosumer-level lenses in the 18 - 200mm class are great all purpose lenses.
So zooms are there to use - but you should be aware that zooming does more than provide a wider field of view or bring something closer together. Changing the focal length on your camera changes the perspective.
Need proof? Look at these two images:
Dramatically different, you say? Actually, they were shot from pretty much the same direction and were focussed on the same point. But notice how much closer the background appears to be to the playground in the first shot, compared with the second. Notice also, how the swings frame seems to be at a much greater angle in the second shot, compared with the first.
The first image was made on a Nikon D800 at 200mm ("long" or telephoto) focal length, while the second was made with a focal length of 18mm, which is a "wide" lens. Both images were made with the same exposure, and were pretty much at the same angle to the playground. I simply moved closer in the second shot to ensure the frame was filled by the swing.
The fact is that by using a "short" lens, as with the 18mm shot, we do more than simply get a wider angle in our shot. It also makes things seem further away - and deepens the depth of field of the image too. Great for landscapes, but it will make distances seem greater than they really are.
"Long" lenses, such as the 200mm shot, do the opposite. Objects seem closer together - as you can see with the first shot. Long lenses compress the image. And long lenses produce a shallower depth of field than short lenses.
Some times, we don't have any choice. When photographing a lion, it's a better to use a long lens than to get out of the car and walk up within striking range for a nice close up. Conversely, using a wide angle lens when capturing a landscape makes more sense than backing up a kilometre of two to get the whole scene in the shot.
Portraits are usually (but not always) made with a lens with a longer than standard focal length. Classic portrait lenses are in the 85 - 105mm range because this generally provides a natural look.
But these "rules" don't always apply. (This is probably the rule of photography: the rules may not necessarily apply.)
This portrait of my friend Claude was made with a 38mm lens, and I'm very pleased with the result! He doesn't look weird - largely because I didn't get too close. (If you want to see how a short lens will distort a portrait, check out Arnold Newman's famous portrait of Alfried Krupp. It's a classic example of the deliberate use of a short lens.)
On the other hand, long lenses can be used in landscape work. I've been complimented on the landscape below, which was captured with a 200mm lens on a Nikon D300. (The body is significant because it has an APS-C (or crop frame) sensor meaning that the focal length of the lens was effectively 300mm - an actual telephoto lens. The kind of focal length used for wildlife work.)
I chose that lens to pull the headland in closer - and to "compress" the image to provide that sense of immediacy and closeness to both the headland and the surf.
I think it works.
So there you are. Use the zoom on your camera by all means. Sometimes you have no choice, but it's important to understand that using a particular focal length will affect your image.
It's important to know how your choices change your images - and the best way is to experiment.
And sometimes, it's better to zoom with your feet!