What camera lens should I purchase for shallow depth of field?

I own a Nikon D3100 (18-55 mm lens) and I really want to do more with my camera than what this lens allows. I'm looking for a lens that will give me really shallow depth of field, any suggestions? In addition to purchasing that lens, I'm also looking to purchase a zoom lens. Any suggestions for that, too?
Price is definitely a factor, but I do want good quality, so I'm looking for a good compromise.

I would first try shooting with that lens at the maximum aperture before investing money in another lens.

Depth of field, or creative control of depth of field, is a function of:

1) Size of image on sensor/film. The larger the sensor or film, the shallower depth of field.
2) f-stop. A 2.8 lens wide open will have more depth of field than a 1.2 lens wide open, all other things being equal.
3) Subject distance. The close the subject to the sensor/film plane, the shallower the depth of field.
4) Final magnification. An 8x10 will have shallower depth of field than a 2x3 print, assuming the viewing distance is the same.

So, if you are doing macro photography, most lenses will have a shallow depth of field.
If you are doing wide angle landscape photography, you will need a tilt/shift or distortion control lens to allow you to manipulate the area of focus.

The final answer, that is not really an answer, but it sort-of leads in the right direction: 200mm f2.8 lens (or a zoom that has 2.8 when zoomed to 200mm, would be a good start.

Best bet is to purchase a NIkon lens, the longer the better, because when you shoot at full telephoto and with the lens wide open (largest f/stop like 4.5, or 6.3 ot what ever) the shallowest depth of field results!

P.S. If you are looking for people pictures a 24mm (which is wide angle ) will not give you pleasing results!

Nikon has recently announced a new 50mm f1.8 AF-S, and that will autofocus with your D3100.
http://www.dpreview.com/...mmf1p8.asp
This will cost about half as much as the 50mm f1.4 AF-S. It will cost more than the currently available 50mm f1.8 AF-D, which will not autofocus with your D3100.

Before I go on there's one thing you should know. You can do anything with any lens. You just have to understand its limitations. You can take a wide angle shot with a telephoto lens if you back up far enough. You can take a closeup with a wide angle lens if you stay close enough. You can blur the background if you position your subject as far away to the background as possible with you staying as close as possible to the subject.while using the smallest f/number on your lens. It just so happens that there are lenses that can do some jobs better than others. Don't put your kit lens down. It's a good one if you know exactly how to get the best out of it.

You could try the Nikkor 50mm f/1.8

It can be had for about $120 at the most.

I would also recommend the 50mm f-1.8 lens. Great shallow depth of field makes it an excellent portrait lens.