The most common lenses everyone tends to get are:
1) a walkaround zoom
This is a wide-to-normal or normal-to-short telephoto zoom lens that's good for landscape/portrait/snapshot photography. Your basic vacation shooting lens. The main choices you go for here are the focal length range and maximum aperture. If you want to shoot indoors without a flash, you want an f/2.8 zoom. This category of lenses probably has the largest number of choices in any lineup.
2) a portrait lens.
Usually a nifty-fifty, but different folks have different working distances. Typically, though, this will be a 35mm, 50mm, 85mm, or 135mm fast prime lens with a max. aperture of f/2 or larger (smaller f-number. Commonly, f/2, f1.8, f/1.4 or [if you're really really rich and don't mind huge lenses] f/1.2). The wider aperture lets you use the lens in lower light and gives you a narrow DoF with lots of bokeh (out of focus blur) so that you can focus the viewer's attention to a specific spot of the photo with selective focus.
3) a telephoto zoom
Long reach for faraway subjects. The most common telephoto zoom lengths are 70-300 and 70-200. This is useful for sports, wildlife, or just stuff where you have to hang back and can't get closer. Again, your main choices are going to go by focal length and max. aperture. F/2.8 if you want to shoot indoors without a flash, and more commonly f/5.6 at the telephoto end of the zoom if you want a small price tag.
Stabilization is a bigger issue with telephotos because the longer reach magnifies camera shake. The rule of thumb is that you want to shoot with a shutter speed of 1/
focal_length or faster. So, with a 70-300 lens @300mm, you want a shutter speed of 1/300s or faster. With f/5.6 as your widest aperture, that probably means outside on a sunny day with an iso of 400 or more. With stabilization you can ease that handholding limit a few stops. But stabilization only helps with camera shake--not with freezing subject motion. If you plan on taking fast-action photography (birds in flight, sports), etc., you may be shooting at 1/focal_length or faster anyway, and stabilization then becomes, well, useless, and max. aperture or a body that offers high iso settings may be more useful.
Some folks will use an f/2.8 zoom for portraits if they have to move around a lot and need the framing flexibility (e.g., shooting weddings). Some wildlife photographers will use supertelephoto primes for image quality (e.g., 400mm, 500mm, or 600mm lenses), but those tend to be more specialized uses than general. Also, some people are willing to compromise image quality and get a superzoom (wide-to-telephoto, like an 18-200 or 18-250) for convenience and lower cost.
Other less common lenses folks like would include:
1). Macro lenses (allow for very close focusing. Usually used for flowers and insects and tabletop items).
2). Ultrawide/wide-angle lenses--mostly for landscape shooting but also useful in small venus and for large groups of people where your ability to run backwards is limited, and you want to grab more of the view.
3). Fisheye lenses--mostly for skateboarding
because of the funky distortion, but gives you an extreme funhouse wideangle with barrel distortion. Also useful for scientific work and spherical panos when you need to capture an extremely wide angle of view. The two main kinds of fisheyes are diagonal (where the entire frame is covered) or circular (where the image is a circle within the frame).
4). Tilt-shift lenses--allows lens "movements"; similar to old-style view cameras with bellows. Can be used for perspective correction and DoF manipulation. Mostly used for architectural photography (to straighten out and make lines parallel rather than converging to vanishing points) and product photography (to increase the DoF in macro shots), but increasing being used in making "fake" macro shots, where subjects appear to be small toy models with a very thin DoF.