Hi There
I hope that this information may be of use to you.

The advice is based on my own experience with a limited number of graphic tablets but a relatively wide selection of software.

There are some links below, and elsewhere on the page, that may provide more help.
Fishpond Australia
600 x 120 skyscraper
I have just noticed that search engines are sending people to my site when they ask about buying a graphics tablet. So here, hopefully, is an answer to that question.
This is not a question that can be answered with a simple yes/no answer. Also this advice is based on my own personal experience, with just two models of graphic tablet from one manufacturer (now three from two manufacturers), but hopefully it will give you some pointers, to help you decide for yourself.

Couldn't live without it.
Let me say first of all, that I could never go back to working without a graphics tablet, though for some tasks, I still find the mouse the best tool to use. It really depends what I am trying to do at the time.

Tablet works as a mouse.
A tablet can perform all of the functions of an ordinary mouse, pointing, clicking, right clicking and double clicking, drag and drop etc. One of the things that it can't do is emulate a scroll wheel. Whenever I am browsing the web or using any software that is easier to do with the scroll wheel, then I always use the mouse.

Drawing and painting software
When I am working with drawing or painting programs, I use the graphics tablet about 90% of the time and the mouse for the rest. Sometimes the tablet just appears to be over sensitive, where the mouse works just fine (don't forget all of these comments apply to my tablet, others may work differently). Check out my gallery pages - much of the work was done with a graphics tablet.

3D Modelling
I tend to find that for 3D modelling I use the mouse just about exclusively, especially if I am using Blender, which makes heavy use of the middle mouse button (Blender by the way is a free 3D modelling program, find out more on my Blender pages)

3D Modelling update (November 7, 2007)
I have recently been using some newer 3D apps (Curvy 3D and MOI) which are more suited to use with the tablet, actually MOI (Moment Of Inspiration) was designed specifically for the graphic artist/tablet user. I can report that these newer apps work well with the tablet. Also Caligari Truespace has a setting to make it more useable with a graphics tablet, well versions up to 6 definitely do. I don't know about version 7 or 7.5 as I haven't tried those.

Web page creation
When creating my web pages, I use Macromedia Dreamweaver, and use only the mouse. The scroll wheel gets a heavy workout, as I scroll up and down trying to find all of the errors on the page.

Web page creation update
I have gone back to using a text editor (with syntax highlighting) for creating and modifying pages. Now that CSS is used for page layout, instead of tables, I just find it quicker and easier than using IDE's such as Dreamweaver and Microsoft Expression Studio.

I used PSPad for quite a while but have now switched to CodeLoster PHP Edition but I still find it is the mouse that gets used, rather that the graphics tablet.

Animation
The tablet and the mouse probably get about an equal share for this task. The tablet is used when I am creating the drawings, but the mouse takes over as I move things around, work in the timeline and everything else involved in the animation process.

Using Office programs
Here I am referring to word processing, spreadsheets etc. I don't really do a great deal of this as my main area of interest is in multimedia, but when I do, the mouse is usually used exclusively.

Music Software
Once I have got the music into the sequencer, with the midi keyboard, the mouse is usually the most used tool for arranging tracks, setting instruments etc. etc.

Signing my name
I often sign my digital paintings/drawings and the only way to do this is with the pen and tablet. If you don't believe me, just try signing your name with your mouse.

Handwriting Recognition
I have only added this because a few people have e-mailed me asking which pen works best for handwriting recognition. Actually I have never tried this on the PC. I did play around with it on a Casio PDA that I used to have but to be honest my handwriting is that bad that i am sure that I can get more text entered even with my unorthodox four fingered typing style (I have gradually improved from two fingers to four, sometimes even five). So unfortunately I can't give any advice at all on this subject, sorry.

Handwriting Recognition (update)
I recently played around with the handwriting recognition in Microsoft Word for a short time and it worked rather well. I was quite surprised that my scrawl was recognised.

Summing Up
Basically if you are doing anything that is done with a pen, pencil, paintbrush, chalk etc. as a non-computing task, then the graphics tablet and pen is the tool to use.

If you are doing things that you normally do with your hand, or finger, e.g. picking things up, dragging things around, pointing to things, then when using the computer, a mouse usually works best.

So what about finger painting?
I'll let you decide, but my money would be on the graphics tablet.

What I Use
Until fairly recently, I have only ever used Acecat tablets from Acecad. The first one was not pressure sensitive, and had a cord sticking out of the end of it. It had to be connected to both the serial port and the keyboard through an adapter. It cost me $AU 349 but it was the best that I could afford at the time. It was still better than the mouse for drawing and painting.

My second tablet, an Acecat Flair is pressure sensitive, cordless and just plugs into a USB port, though it does need a battery (AAAA, yes quadruple A). This tablet cost me $AU 99 on sale, down from $AU 149 (bargain!)

Both of the above tablets had approximately a 5" x 5" drawing area.

I am now using a Wacom Graphire tablet (see below) which has more or less an A5 drawing area.
Update 1
I've just bought my first Wacom tablet (a Graphire 3). I will let you know how it goes when I've had time to evaluate it.

November 2004- October 2007
Well I have been using the Graphire tablet for a while now and I am very happy with it. It is performing well with all of the applications that I use a tablet for, and some programs are working better. Specifically, "Toon Boom Studio V2" was so slow as to be almost unusable with the AceCad, but it works fine with the Graphire.

Another animation program that wouldn't work at all with the AceCad was "The TAB 2.0", once again this program works just fine with the Graphire (well actually it didn't work with the drivers that came in the box, but downloading the latest drivers from the Wacom site fixed it).

I believe that most graphics software companies test the Wacom tablets with their applications but I don't think that many of them test with other tablets.

One feature which the Graphire has, which the AceCad didn't have is the eraser mode, this allows you to switch to the eraser just by turning the pen upside down (as long as the software supports it). Now that I have got used to this I wouldn't like to do without it.

The other big advantage is the fact that the Graphire doesn't use any battery in the pen. It could get rather frustrating when picking up the AceCad and finding that the battery was dead, even more so if I had forgotten to replace the spare in the cupboard, a AAAA battery is not the sort of thing you can pick up at the corner shop, or in my case the village store.

I hope that this extra information may be of help to you but don't forget these comments apply to my computer and the way it is set up. I do have a large amount of software installed and as I also dabble with computer music, I also have extra hardware hanging off my machine.
Update 2
About 12 months ago (August 2011) I began to evaluate the new Wacom tablets, which featured pen and touch. This made it possible to draw with the pen, or move/rotate/zoom the page, using a couple of fingers. I was vey impressed and was on the verge of buying one, when I switched tack completely, and bought an iPad 2 (see my iPad blog).

If you are still using the desktop PC for your art, then I would definetely buy a pen and touch tablet. Of course you may decide to go with a tablet computer, and that is a whole new ball game and one I don't intend to cover here, except to say, I love my iPad.

Whatever you decide, I hope that this information is of some help, but more importantly - Have Fun