I have the 50mm/1.8 and have to say that it is a dream for portraits, indoor shooting, and other low-light situations. As others have mentioned the DOF is incredible. I took a fairly close full front shot of my son at f 1.8 with this lens. Upon viewing this photo in Lightroom I was pleasantly stunned to notice that the tip of his nose was in focus but his eyes were slightly blurred. No, he doesn't have an abnormally long nose either!
I also own the Tamron 18-270mm lens that was mentioned earlier. This lens is also unbelievable, however, it is not without it's flaws. These flaws are not uncommon across the range of super zoom lenses though. Perhaps the most annoying thing for me is the AF is somewhat wonky/finicky. All in all though, I have so far found it to be a capable do-it-all lens. I haven't had it too long so it remains to be seen if it will truly become my go-to lens. For now I stick with the Nikkor 50mm when indoors, and use the Tamron for times when I need the zoom.
Finally, I very rarely will use the kit lens. I will probably sell it if I can, to be honest.
I cannot stress how good the 50mm Nikkor lens is for indoor and portrait shots. It's not a very pricey piece of gear either. You should definitely check one out, you won't regret it!
Update: I returned the Tamaron for a credit and bought a 55-200 VR and paid a little extra for a 60mm micro. I couldn't get over the cheap feel of the Tamaron, and I found the action to be uninspiringly stiff.
Also, don't listen to everyone saying that 18-55 kit lens is no good. I own it, and it is actually a pretty decent lens - if you take into account the price, it's actually an excellent lens. Experiment with the lens, and how to take advantage of its strong points, and you'll find that you are taking beautiful pictures in no time with it.