Along with a good mid-range zoom lens and a wide-angle zoom, a telephoto zoom will round out your collection of lenses quite nicely. A telephoto lens will zoom in further and magnify the subject more than a typical mid-range kit lens. This makes them great for "reaching" those far away subjects like wildlife, sports and even detail shots on landscapes.
This is 200mm on a full-frame camera (equiv. to 125mm on a small-frame)
When selecting a telephoto zoom lens, you'll have to consider a few things (in addition to budget). First, the higher the focal length number, the more "zoomed in" the lens can go. Meaning, a 70-200mm lens won't reach as far as a 100-400mm lens. So if you need to reach as far as possible, go for the higher focal length number.
You'll also want to look at the lens' maximum aperture. The maximum aperture is the widest the aperture can open on the lens. A wider maximum aperture will let in more light and, thus, allow the camera to use faster shutter speeds. So if you think you'll need fast shutter speeds when using the lens, you might want to consider getting the lens with a wider maximum aperture. The lens' widest maximum aperture is always indicated in the title. For instance, the Canon 70-200mm f/2.8L IS II lens can open all the way to a maximum aperture of f/2.8. Whereas the Canon 70-200mm f/4L IS can only open to an aperture of f/4. To learn more about how to understand lens nomenclature, check out this post.
Here are the telephoto zoom lenses I recommend:
Canon EF-S 55-250mm f/4-5.6 IS (buy - $255)
A great starter lens for those looking to get a little more reach out of their Canon DSLR. It's a mere $255, which shouldn't break the bank for most people, and it zooms pretty far out to 250mm. Although this isn't as far as the next lens, which reaches to 300mm, 250mm ain't half bad for a lens under $260. At this low of a price, though, the autofocus motor isn't as fast or as quiet as the more expensive lenses. But at least it has image stabilizer, which is a very nice perk on long lenses like these.
Canon EF 70-300mm f/4-5.6 IS USM (buy - $549)
This lens has a few benefits over the 55-250mm discussed above. First, it reaches 20% further out to 300mm. When photographing wildlife or sports, that extra 50mm turns out to be quite a bit. The build quality of this lens is a little bit better over the 55-250, too. Sure, it's no magnesium-alloy tank like the professional series lenses, but it will feel a little more robust than the 55-250mm. Most importantly, this lens features Canon's Ultrasonic Motor (USM) auto focus system. That means this thing will focus much, much faster and much more quietly than the 55-250.
For your first high-end option, I'd recommend the Canon 70-200mm. At 200mm this lens really doesn't reach that far. Truthfully, it just isn't enough zoom for most wildlife photography. But for sports and portraits...it's phenomenal. That being said, Canon offers both a 70-200mm with a maximum aperture of f/4 and one with a maximum aperture of f/2.8. Both varieties come with or without image stabilizer, too (get it with stabilizer included - no doubt about it). As part of Canon's L-series professional line of lenses, both feature Canon's top-of-the-line optics, construction, weather-sealing and ultra-fast USM auto focus motors.
But now the real question: do I get the f/4 or f/2.8 version? Here's my short, no-nonsense recommendation: If you want to shoot portraits or sports and you won't have to hike long distances with this lens, get the f/2.8. The 2.8 max aperture will let in 1 stop more light than the f/4, which may be the difference between a shutter speed that's just fast enough or one that's just a little bit too slow for sports. And as for portraits, the ultra-blurry background at f/2.8 will make you drool. But if you're planning to use this more for photographing detail shots in landscapes or if weight will be an issue for you, go with the f/4. It's over a pound-and-a-half lighter than the 2.8 and it's only 1 stop loss of light, which is usually no big deal when shooting still subjects. Oh, and it's over $1,000 cheaper.
High-End Option 2
Canon EF 100-400mm f/4.5-5.6L IS (buy - $1,699)
If wildlife is your thing, then I'd recommend the Canon 100-400mm f/4.5-5.6L. It reaches over twice as far as the 70-200mm and features the same pro-level build, optics, weather-sealing and image stabilization. At 3.04 lbs, it's no lightweight, so be prepared. But hey, the 70-200mm f/2.8 discussed above still has a quarter of a pound over this baby. The extra reach here will be worth the loss of light (which is actually quite a bit). And with today's modern cameras going up to 6-digits on the ISO in some cases, the lack of light won't be much of an issue.
Nikon AF-S NIKKOR 55-300mm f/4.5-5.6G ED VR (buy - $397)
Much like the Canon 55-250mm discussed at the top of this post, this Nikon 55-300mm is a great starter lens if you're looking to zoom in a little further for sports, wildlife, portraits or kids. It has Vibration Reduction (which is Nikon's brand of image stabilizer) and has a decent auto focus motor. Truth be told, though, this thing feels pretty chintzy in your hand. The focus rings always feel loose to me. I really think this lens should run more around $275 than $397, but again, good for starting out. It'll last you a couple years or less, then you can graduate up to a more rugged lens.
Nikon AF-S VR Zoom-NIKKOR 70-300mm f/4.5-5.6G IF-ED (buy - $587)
This is a great mid-level telephoto that works perfect for those photographers looking to shoot the occasional kid's baseball game or the local air show. Like all lenses in this mid-level price range, it won't let in a ton of light, which may become an issue when photographing in dim environments, but the price and weight are just right for the casual shooter. The build quality is slightly better than the 55-300 above, but the zoom and focus rings still feel loose to me. It also has Vibration Reduction to help combat camera shake.
High-End Option 1
Nikon AF-S Nikkor 70-200mm f/2.8G ED VR II (buy - $2,397)
For close-range sports, portraits and scenic details, the Nikon 70-200mm is a superb choice. Its max aperture of f/2.8 will let in a boatload of light, allowing you to use faster shutter speeds and/or lower ISOs - perfect for capturing action. The build quality is leaps and bounds above the mid-level lens discussed previously. Rugged construction and weather sealing ensure this lens will go to hell and back with you, and never miss a shot. The optics, of course, are top-notch and the Vibration Reduction will be a godsend when handholding this puppy. It's pricey, but you won't need to replace it for years and years.
High-End Option 2
Nikon AF VR Zoom-NIKKOR 80-400mm f/4.5-5.6D ED (buy - $1,679)
If you need more reach than the 70-200mm can give you, the Nikon 80-400mm may be your best bet. It's rugged, tough and sharp - all good things when it comes to photographing wildlife. And with double the reach over the 200mm, you won't find yourself wishing for "more lens" as often. Don't get me wrong, though, you'll still want "more lens." Wildlife always leaves you wishing you could reach further. The loss of light with the smaller max aperture may be an issue when photographing in dim environments, but with ISO performance the way it is on newer cameras, it won't be a problem most of the time. Be prepared to carry the weight of this beast, though.