Can't speak so much for Canon, but with Nikon they have a very good range of average "walk-around" lenses. 18-55, 18-70, 18-135 and 18-200. These are typically "kit" lenses. I have the 18-70 and the 18-135 (which I just picked up recently). I used the 18-70 for over a year, but really wanted something with a longer reach. The 18-200 is great because it also has VR (vibration reduction), but is expensive and hard to come by. These are not "fast" lenses as their f/stop range starts at f/3.5 at the 18mm end and then gets smaller (f/5.6 at the 135mm & 200mm range). I like the convenience of the wide 18mm end and being able to reach as far as the 135mm end.
There are also more expensive "fast" lenses within that zoom range. Nikon has a 17-55 f/2.8 as well as an 18-35mm f/2.8. The f/2.8 is constant throughout the zoom range, thus making these lenses more expensive (upwards of $1200). They typically produce sharper images than the lesser expensive zooms and are better in low light conditions because of the wide aperture.
For the medium to long telephoto zoom, I have a 70-300. Again, not very fast at f/4.5-5.6, but it does have VR so it works better than most in lower light conditions (with a non moving subject) and also I don't get any camera shake from hand holding at the long end which I like as well. If you were to get a 70-200mm lens, then your talking again about an f/2.8 (or in a few cases f/4) constant aperture, which again adds a lot of money. They are shaper lenses than their smaller aperture counterparts. Least expensive 70-200mm f/2.8 lens is a little under $800 and that is for the Sigma brand. Nikon and Canon's version with VR/IS go for as much as $1700. My 70-300 with VR was $550. There are non VR 70-300mm lenses for a little as $150.
I also have the inexpensive 50mm f/1.8 prime lens. This lens is very sharp, especially in the f/4-f/11 range. It does very well in low light situations as the aperture opens up to f/1.8, however the drawback with this wide aperture is that your focus has to be spot on because it lacks depth of field.
Lastly I have a 90mm f/2.8 macro lens. Again the wide aperture of f/2.8 which is handy in low light situations (very good for indoor sports, though an 85mm f/1.8 might be a bit better). Also because its a macro lens I can focus on a subject as close as 3 inches away. With my 70-300mm I can only get as close as about 18 inches.
This is a quick rundown of just what I have to give you a bit of an idea. Though keep in mind that everyone has different needs and wants (and wallets

) so you may find other lenses your drawn to. For landscapes a super wide angle might be appropriate, like Sigma's 10-20mm, Nikon's 12-24mm, Canon's 10-22mm. If outdoor sports, then consider the long zooms, 70-300, 70-200, 200-400, 80-400, 50-500. Keep in mind these types of lenses are expensive and BIG.
A good recommendation is to start with a "kit" lens, they're generally less expensive, but gives you something to go with. Once you start getting into photography and you develope your style and what you like, add more lenses from there. Once you get the dSLR bug, there is no cure. Your lens addiction will go on forever. There will always be another lens that you'll want.
Happy shopping.