Zoom, simply means a lens that has a range of focal lengths, meaning it can very from wide to not-so-wide. I would assume by your question that you want a more telephoto lens, or one that has a longer "reach". Before recommending, you should answer what you really want that longer "reach" for. If it is sports photography, you will get one type of lens (fast), if it is for landscapes and such, speed isn't important.
Do you have a price range in mind? As you may know, you can spend anywhere from a few hundred dollars up to a few thousand on a telephoto lens.
Now a few things about the lenses you questioned:
55-200: This is also considered a kit lens. Nikon kit lenses are generally good for snapshots and taking decent photos. I would recommend getting the VR version, as this may help reduce some motion blur, depending on the type of photography you are doing.
18-200: Jack of all trades - master of none lens. When I first bought my D5000, this was the only lens I bought. I thought it would be better to have one "do-it-all" lens than have to carry multiple lenses. Depending on what you are photographing, it can be a great lens. I have this lens and am very happy most of the time. Image quality is good, but no where near great. It has some strong lens distortion issues (any lens with this large of a focal range (zoom) would have some issues). It isn't very fast, but if you know the limits of it, it is a great lens. For travel, and not knowing what you are going to take pictures of, it is good.
A better lens suggestion:
70-300 VR 3.5-5.6: This lens is a little better than the 55-200, and has the capability of working on full frame, should you decide to upgrade to that at a later date. It is big, but not so big that you can't carry it around all day. It is certainly lighter weight than a professional lens. If you are looking for a longer telephoto (zoom), this one would be good, without breaking the bank.
Best overall telephoto:
If you have the money and really want to get great pictures. You really should look at a professional 2.8 zoom such as the 70-200 2.8. This is truly an amazing lens. It is big, heavy, and expensive. If you buy one of the more recent models with the AF-S motor, it will focus on your camera. For an all-around great zoom, you will never need another telephoto lens (unless you get into sports, then you will need expensive long telephoto primes....). This lens will also work later if you decide to upgrade to a full frame sensor camera (D700, D3, etc).
You do not want to buy a device that screws onto the front of your existing lens to "get you more zoom". These will severely impact image quality. The reason you purchased a DSLR is to have the option of changing lenses. Get a new lens.
You should also pick up a few books on photography. There is a lot to learn. DanFinePhotography has a great comment in buying a prime lens. It will really force you to concentrate on composition of your photo, and they all are going to be much sharper and better glass than any zoom lens. For your camera, an inexpensive and good prime lens to start with is the 35MM 1.8 AFS. It is a great buy at $200.00 or so. I will be getting one soon to supplement my 50 MM prime.
Be sure to come back here and post some of your pictures, and we can help you become a better photographer.
Welcome to the forum, and go out and start shooting.
-Andy