Here's my advice to, and answers to frequently asked questions from, beginning photographers. I asked many of these when I was starting out in mid-2006, and I've since had friends and folks online ask me. A lot of this is advice from my point of view, but I'll try to be unbiased in my recommendations.
On October 9, 2006, I bought a Nikon D50, my first SLR, second digital camera, and fourth camera overall. My first camera was an old white camera that took 110 film. My second was a Canon Snappy LXII 35mm film camera. My third was my first digital camera, a Canon PowerShot A40. And in June 2006, a few innocent-enough questions to my friend Adam about what "aperture" and "ISO" meant quickly snowballed into a full-blown hobby. I wrote the full story in my blog, including how I ended up with the D50 after eyeing the Canon Digital Rebel XTi pretty hard.
I now have the D50, a shoulder bag, the Nikkor 18-55mm f/3.5-5.6 kit lens, a Nikkor 50mm f/1.4 lens, and a Nikkor 18-200mm f/3.5-5.6 VR lens. I still need to buy an external flash, maybe a couple filters, and then I expect that'll be it for a while.
Note that I'm answering many of the questions below for general purposes, and all are variable based on what kind of photography interests you--what you'll be using the camera for. My answers are for general use, as that's what I use my camera for--informal pictures of friends and family at parties, animals, landscapes, architecture, cityscapes, documentation, etc.
Probably--it's great fun! The short answer is, if you're wanting to get more into photography and achieve cool effects you see in magazines and in others' shots on the web, and can afford a few hundred bucks for a new camera, then absolutely. You can take a lot of the shots you'd take with an SLR on a point-and-shoot, and the same features like VR on an SLR are a lot more expensive than on a point-and-shoot, but at the end of the day, SLR's will always give you better pictures and allow you to take pictures the way you want to take them quickly and easily.
If I could recommend only one site for beginning photographers, especially digital SLR photographers, it would be Canon's digital SLR tutorial. This site is incredible--very vivid, interactive examples, and makes important but confusing concepts very clear, like focal lengths, exposure, and when to use flash. Another is Digital Photography Review, which has the most extensive listing of camera reviews and tech specs I've seen, including a great side-by-side comparison tool if you're trying to decide between a few models.
Next is Ken Rockwell's site. Ken's site is great--he's like the House of photography in that he knows a lot about the science and art of photography, with some amusing meanness and sexism thrown in for color. Though, being an actual person instead of a character on TV, he's not always right, but he IS right that megapixels matter VERY little, and a great camera gets out of your way. Beyond that, he's got a ton of lens reviews and comparisons, and some user guides that explain how he uses cameras. Take his advice (and Canon's, for that matter) as a guide and not written-in-stone law and you'll find them very helpful.
Personally I'd say Nikon or Canon. They're widely regarded as the best brands, and the SLR's most professionals use. There are a ton of great lenses you can buy for them. They've been around a while and will be around a while. I don't have any personal experience with the others so I can't speak to them, but I'm sure any of them take great photos.
One important point in making this decision is that once you pick a make, you'll probably want to stay with it. Nikon lenses can't be used on Canon cameras and vice versa. If I switched from Nikon to Canon for example, I'd throw away all my lenses, flashes, etc. I bought for the Nikon and start over with Canon, or carry around a bunch of duplicate equipment just because it's compatible with one body but not the other.
If you're talking point-and-shoots, the differences aren't as significant. I've used some Canon point-and-shoots and really like them (for the features/usability, not the picture quality--the latter says more about me as a photographer than about the camera), and they're regarded as the best; Nikons seem harder to use.
If you're trying to decide between Nikon's D40, D50, D70s, D80, and D200 for example, or Canon's Digital Rebel XT, XTi, or EOS 30D, you'll be hard-pressed to find much difference in picture quality. Any of these can take great pictures in the right hands. And don't think for a second that the D50 isn't as good as the D80 or Digital Rebel XTi because it has 60% as many megapixels as they do.
A great camera gets out of your way, and in those terms, higher end models are progressively better about getting out of your way. For example, the D40 lets you change shutter speed and aperture more easily than on point-and-shoots. The D50 adds changing ISO and white balance easily. The D80 adds changing focus and metering modes a little more easily, and the D200 more so.
That's the big, and most neglected, part of the "which camera should I get" argument. Otherwise, of course lower-end cameras have fewer features while higher-end cameras have more features that may or may not matter to you. The D40 is incompatible with most of the other Nikon lenses available, which you won't care about if you don't have any older lenses already and plan on just getting 1-2 lenses and not doing anything too technical with it--using it like a high-end point-and-shoot. The D200 has grid lines on the viewfinder and depth-of-field preview, which are nice to have for a lot of people, but I doubt that will make or break anyone's camera decision; its better weather-proofing might.
Try to get your hands on a couple you're thinking about before you buy. This was the deal-breaker for me--I was almost ready to get the XTi over the D50 before I handled them, then bought the D50 after. Someone else said the tiny XTi feels great, and doesn't like the Nikons. With a big SLR, how it feels in your hands matters a lot more than it does with a point-and-shoot the size of a credit card.
Finally, lenses matter more than camera bodies. Save $400 on your body and buy a better lens instead, which will still be great on the next body you get. If you're new to photography as I was, it'll be a while before differences in camera bodies hinder you much--for example, I change ISO and white balance all the time, but rarely focus and metering modes. So I won't grow out of my D50 for a while yet; I'm buying better lenses and so on instead for now.
You should probably just get the kit lens starting out, unless you already have some lenses from older film cameras you want to reuse, or have money to burn and want to get one like the 18-200mm that encompasses what the kit lens offers. After that, the 50mm lens is a popular choice, including the very inexpensive and light f/1.8 one and the faster f/1.4 one; both are good for photography in low light/indoors where it's not practical or preferable to use flash, or if you're trying to isolate your subject and blur the background (a cool effect). VR/IS technology is great, so consider a telephoto zoom with VR like the 70-300mm, faster 70-200mm, or super zoom 18-200mm. Apparently another popular choice is a wide-angle zoom like the 12-24mm, but as I haven't won the lottery yet, I haven't bought one.