You are about to buy a digital camera, and you are wondering what else you will need.
First, more memory. The memory card that comes with your camera is not going to be enough Plan on buying one or more 64Mb or 128 Mb cards. Having trouble rationalizing this extra expense? Think of it as film that you can reuse. In fact, camera memory these days will pay for itself in its second use, compared to film. Get the type compatible with your camera, usually Smartmedia or CompactFlash.
Second, rechargeable batteries and a charger. Many digital cameras will accept alkaline batteries, but only use these in an emergency. You will get very few shots on a set of batteries. (Don't throw those "dead" alkalines away -- they are still good for use in most anything else.) Unless your camera has a built-in lithium ion battery, what you want are NiMH rechargeables. They last much, much longer per charge than alkalines, and you can use them over and over again. Check out Radio Shack, Sam's club, and Thomas Distributing. Always have a spare set of batteries. Do not buy a camera without determining what kind of batteries it uses and what it costs for a spare battery. Without spare batteries, you will shoot far fewer photos as you try to save your batteries for the utimate photo opportunity.
If your camera does not have a USB connection, or if it has one but does not appear like one more hard drive to your PC, you should get a memory card reader. This is like an external drive for your memory card. The cards that connect via USB are fast and convenient, and will allow you to use nearly any software for transferring images. If your camera has only a connection for the serial port of your computer, this item is a necessity. They generally run around $30. Sandisk, Lexar, and Microtech make good ones. They are about the size of a computer mouse.
Those are all the necessities. Now for the luxuries to ask for on your next birthday.
Photo Editing Software. Did you ever dream of doing creative darkroom work but could never justify the time, space, or expense? A good photo editing program will let you do amazing things. See the companion page, What software should I get?.
Panorama software. Panoramas can open a whole new world for you. Some software is even free. See Creating Panoramas.
A monopod or tripod. These are great for stabilizing the camera for telephoto shots, particularly in low light. Never thought about a monopod? I use my monopod ten times as much as my tripod. It is compact, lightweight, doubles as a walking stick, and does a nice job. I recommend the Bogen 3006.