Comment Figure Out Your Uses and What You'll Love About It (Score 1) 569
This thread already has great posts in it. I'm an amateur who has recently done a good bit of research and made some purchases.
Prior to this 2011, I usually kept a small point-and-shoot around for a few years at a time. Each one took some great photos, and plenty of throw aways. That was until I had a chance to use a friend's Nikon D40, an older 6MP DSLR. I discovered with it that I had far more control, especially over focus and depth of field. All of the sudden, I could put the subject into focus quickly, and I found I was getting better results. From this experience, I went on a research binge and ended up making two purchases soon after. I bought a Canon ELPH SD4000 IS, a Point-and-Shoot that works well in low light, for my girlfriend. I got a Nikon D3100, an entry level DSLR. Here is a quick list of what I learned.
1 - The world is full of great cameras. A good photographer can make great work with most or all of them, and the best camera can't make up for a poor photographer.
2 - The DSLR world is as much about lenses as camera bodies. Canon and Nikon seem to be the two that most folks are religious about, and both have their mutually-incompatible lens styles. Every dollar toward one lens style gets you further invested in that family of lenses. It's not a bad thing, but you'll want to school up if you go the DSLR route. Have a sense for how the UIs work, the lens options (including compatibility with cameras), the relative prices, etc.
3 - Despite my Nikon D3100 having 14MP and all around "better specs" in most regards, I have little practical benefit to having my DSLR vs. the one borrowed. I get the joy of having more control with both, and I know I can shoot photos that could be printed to be somewhat larger. Scaling images down, my photos might be slightly more forgiving than those of the D40. In truth, if I were taking the same photos with either, I would have the same keepers.
4 - DSLRs carry a stigma in crowds. Carrying a point-and-shoot, you can take your pictures and put them away. Pulling out a DSLR means everyone around knows they're on camera.
5 - The Canon SD4000 IS does the best of job of no-flash low-light shots of any point and shoot I have seen. It does better than my DSLR with stock lens due to having a lower aperture. If your shots are mainly of people indoors at their homes, in restaurants, at clubs, or in other night settings, pulling out a DSLR will not only inspire poses or turned backs, but will probably require more tuning. I am not endorsing this camera as the best at this, but only that I was satisfied that I matched the camera to the kinds of shots that would be taken. I would have been less happy with a general purpose point and shoot.
6 - I have no experience with the "DSLR-like" cameras in the mid range, except that very good photographers I know downsize to these to have a camera that they can take with them anywhere.
7 - Borrow a camera if you can. I was very happy that I did.
Once you know what you'll use it for and what it is that encourages you, you'll be in a better position to figure out what camera will fit you.
Good Luck!