Whether you're a beginner or an experienced artist, shopping for a tablet can be one of the most individual, confusing experiences out there. There are so many different kinds at different pricepoints, but be aware that as a general rule, tablets are 'get what you pay for'. What you need will depend quite a bit on what you plan to do with it. If you're a casual doodler, you likely won't need a $400 dollar Intuous, much less a $1600 dollar Cintiq.
The first thing to figure out is your personal preference in regards to drawing on a traditional tablet, or if you're more comfortable drawing directly on a screen. Just be aware that the latter options, while lacking the mental disconnect between screen and where you draw that normal tablets have, are often far more expensive. I highly recommend doing everything you can to test between the two types before deciding to make a purchase, but if you are unable to do so there are many cheap traditional tablets you could try just to get a feel for it.
For easy reference, I will refer to the type of tablet that you draw on which is separate from your monitor as a 'traditional' tablet, and the type where you draw on it directly as a 'cintiq-type' (as that's most recognizable for people).
For beginners, here is a small list of cheap, traditional tablets I have heard of that you may wish to try, all under $100:
Wacom Intuous Draw
Wacom Intuous Refurbished
These are small, cheap tablets that would be good for beginners to try while they work to get used to digital art and the disconnect between the tablet and the screen.
If you are an artist who is looking to upgrade from a cheap traditional tablet to something better, my -personal- recommendation based on experience is the Wacom Intuous 4. I took art as a contract job for a website and needed something better than what I had, and have not regretted my purchase since. My only complaint would be the rough surface texture, which will eat through your nibs, but I got around this easily via a screen covers.
The Wacom Intuous series are widely regarded as the best tablets on the market, thus the expense.
There are many options, however, and many artists will go through a couple of tablets before finding one that suits all their needs, so don't be discouraged if it takes you a few tries. It's usually fairly easy to re-sell a lightly used tablet or to donate them if you're feeling generous.
As for cintiq-type tablets, you may be able to try them via display models at stores. Unfortunately, unless you manage to find a good deal for something probably refurbished or heavily used, you are unlikely to find one that won't cost at least a couple hundred dollars, which is a costly gamble to take for something you might not like in the end (I have tried cintiqs and personally didn't care for it, myself). I would definitely recommend at least making a real effort to get used to traditional tablets before giving up, as it can a while. It took me over a year to get the hang of one!
I am now opening the comments for discussion over people's experiences and recommendations for tablets so this can become a post that is a good resource for new and not-new artists! What tablets have you tried? What were the pros and cons? Are you looking for recommendations based on your needs? Go for it.