Tripod
Even the best photographers will not trust their steady hands. Every photographer should have a tripod. What kind of tripod you get will depend on your needs. Those with point-and-shoot cameras can probably get away with small light-weight tripods that can easily fit in your camera bag. If you have an SLR, you'll want to make sure your tripod is strong enough for your camera. Don't forget to take the weight of your lens into consideration. You don't need to spend a whole lot of money to get a good tripod. There are high-end tripods with replaceable heads, carbon fiber shafts and all sorts of bells and whistles. But don't spend money on those until you know you need it.
Tools
You should carry a small set of tools with your camera at all times. Pray you never have to use them in the field, but if you need them, you'll be glad you have them. You'll want to get yourself some small precision screwdrivers, a cleaning cloth, a blower brush, some lens cleaning fluid (made for cameras, not the stuff you use on your eyeglasses), some tape and a few small wire paper-clips (they come in handy sometimes).
Commonly Overlooked Items
There are a number of things that are often overlooked. These aren't necessarily items that you will always want to carry with you. But you may want to create a little kit to keep in your car in case certain circumstanced were to arise.
Raincoat & Umbrella
Foul weather can be very beautiful subject material. That said, you'll want to protect yourself and your camera. Always be prepared.
Large Flashlight
My recommendation would be to get a D-Cell Mag® Light. They're virtually indestructible, and they provide a lot of light. Not only is it good to have in case you need to be out at night. But it can be useful in your work.
Notepad & Pencil
Meta data within digital photos make easy work of tracking details such as F-stops and shutter speeds, even your lens and focal length. But if you are serious about learning photography, you'll want to jot down other notes about your photographs from time to time. How did you set up? How did you get to your location? What feeling did your surroundings create? You may even want to make a few sketches of where the sun (or other light source) was in relation to your camera.
Conclusion
It's my hope that this little guide has been useful to you. As I mentioned at the beginning of the article, everyone has their own philosophies. I would like to encourage anyone to offer comments and suggestions. The world of photography can be very rewarding. But you have to learn to think and function like the best photographers. The right equipment (and not having too much of it) will greatly help you create beautiful photographs.