(( Coranda gave some excellent information! It really does come down to how much you are willing to spend and what type of art you enjoy.
Aside from the programs you need, you must also consider the mechanics of how to draw/paint using the computer. The most inexpensive way is of course with the mouse. Unfortunately, this is nearly impossible for many people when doing detailed work like hair, etc. So, you will probably need a drawing tablet which lets you draw directly into the machine. The best and most widely used brand is
Wacom.
A large size tablet is not as important as it might seem, and you will wonder how you lived without one when you get used to it! You might consider shopping used on Ebay too. Be careful, though. With my tablet, I've managed to put a very tiny nick into it, and it causes problems each time I pass over it. So, personally, I'd be scared to buy used, but I know others who have been very happy with their purchase.
As Coranda mentioned, you can use 3D art or 2D (drawing/painting) for your images. There are good and bad points to each. Here are some things I've discovered.
3D Art
-Programs are moderately to extremely expensive.
-They take massive amounts of system resources and are non-intuitive to learn.
-3D has inherant problems which will ruin your images unless you do post work in Photoshop or a similar program. For instance, joints are almost never right the first time. You'll see the tell-tale 3D joint bend which just puts my teeth on edge when I see it. ::chuckles::
-However, 3D can provide you with very decent, realistic images if you are new to art.
-Post work might possibly be done with a mouse, so a tablet is not entirely necessary (but it will make your life easier).
2D Art
- A tablet is pretty much mandatory for drawing in 2D. I've seen one artist who did amazing work with a mouse, but she is definitely not the norm!
-A scanner is helpful when working with 2D. It is extremely difficult to draw directly into the computer and keep the lines clean and sharp. This is especially true if you are working with large, high resolution images. Most people I've noticed will do a traditional sketch, scan it in, then color it in Photoshop or some other program.
-With 2D art, you are not as limited as with 3D. If you enjoy sketching, this may be the way to go for you.
Art Programs
Here are some links to programs and resources which might help you. For the programs, I'll list them from least expensive to ...um...very!
3D
Daz Studio 3D (Available with a free version I think. They still get ya with all the addons you will need, though.)
Poser 6 Fairly expensive after all the addons you will need. Also, buggy and difficult to use. I've used it for awhile and have a love/hate (mostly hate) relationship with it.
You can also google more professional programs which will cost several thousand each. Some names to look for are
Maya
LightWave
3DS Max
2D
Corel Paint Shop Pro A decent little program for only $99.00. I've seen some very fine work produced with this. It doesn't have the bells and whistles of Photoshop, though.
Corel Painter 9 On sale for $329. An amazing program geared toward the traditional artist. Personally, I found it difficult as many of the tools/keys/brushes were very different from Photoshop, so I was constantly frowning and hunting for what I wanted. But, for someone used to traditional art, they give you pastels, oils, acrylics, inks, pencil, even crayon, and more. The settings allow for wet/dry/medium paint on the brushes etc. Really, really great program if you have the patience to work with it.

It is the closest thing you can have to traditional art on your computer.
Photoshop This is pretty much the standard in digital art/photography, but the newest version is expensive. I use CS2 and adore it. I have upgraded over the years, but I know lots of people who are producing professional work with older versions. Many still use Photoshop 7. If you decide to buy an older version used, be aware that many of the cool brushes people are making for the program might not work on your older version. That said, many of the brushes people make aren't really necessary, so an older version might be the way to get started on a budget.
Resources
There are many great artist communities out there. Some are more supportive than others. The best I know of is
Norraths Studio. These are people who play EQ (and WoW and other games) and are artists. Some are professional and some aren't, but they all give very valuable insight to works posted on the board. It's a great place to learn (there is an extensive library) and get feedback on your work.
I hope this helps, and I really didn't mean it to be so long! ))