This is probably one of the most important aspects of choosing a tablet computer. There are different schools of thought on this, and it will depend what you are using your tablet for.
If you want a highly portable device, you’ll want something 8.9 inches or smaller. Additionally this is about the maximum size where the tablet can easily be held in one hand, with 8 inches being slightly more optimal for one handed comfort for most people. This does make the device more convenient to use.
If you want to access high resolution, highly graphical media like complex full websites, comics and magazines a larger tablet might suit you better.
One should keep in mind also the aspect ratio of the screen. For example a 10.1 inch screen tends to be longer rather than wider, which suits Windows, but does not add as much screen real estate as 9.7 inch screens.
If you’re using Windows, the smallest form that you can really use the desktop mode on is 8 inches.
People who use both tend to come to the conclusion that having a larger tablet and a smaller one is best, because they both have their advantages, smaller for portability and ease of one handed use, and larger for the bigger screen real estate. I have used both and enjoyed both. An eight inch can go in a bag easily. But a 9.7 inch is ideal for web pages, magazines, games etc.
For those on a budget, you will need to work out what characteristics are more important to you.
Additionally, if you are inputing a lot of text, you will want a keyboard. For media consumption, tablets are king. But for creation, the desktop still has many advantages. If you wish to enter a lot of text, a keyboard case, or a powered hub are good options (with Windows, and HDMI output, and a powered USB hub, you can plug your tablet into a keyboard, mouse and monitor, using it like a desktop). And if you input text more than use touch only, a hybrid is a good choice.