Camera phones and digital point-and-shoot cameras are fine for taking snapshots, but they're really not meant for "real" photography. Framing everything just so, setting the right exposure, capturing the exact moment in time you want, these are skills you can't easily develop on compact cameras. To get a firm grip on photography and practice the more complicated techniques of the craft, you need to use a camera that offers the full range of settings and, ideally, lets you use different lenses for different circumstances. The vast majority of compact cameras don't even offer PASM exposure modes, and by their nature don't support interchangeable lenses.
Micro Four Thirds cameras are the new kids on the block. They offer the different exposure modes and interchangeable lenses, but are much lighter and more compact than DSLRs.
Canon Rebel XS or the Nikon D3000 camera bodies with included kit lenses. Both models are 10-megapixel cameras that include everything you need to get started on photography. Like all SLRs, they feature full-size through-the-lens viewfinders that are ideal for learning how to traditionally shoot. The Rebel XS also includes a liveview feature for framing shots with the camera's 2.5-inch LCD screen. While they aren't full-frame, both cameras use APS-C sensors that are larger than the Micro Four Thirds format, and generally offer better high-ISO performance.
Canon Rebel T1i
Rebel T1i or the newly announcedNikon D3100. These models include 14 to 15 megapixel sensors, 3-inch live-view LCD screens, and can shoot 1080p video. All four cameras include 18-55mm f/3.5-5.6 lenses. Like most kit lenses, they aren't the best out there, but they'll let you start shooting right out of the box.
Sony Alpha NEX-3
Panasonic DMC-G10, an Olympus PEN E-PL1, or a Sony Alpha NEX-3. The G10 and E-PL1 are Micro Four Thirds cameras, featuring a smaller sensor than entry-level digital SLRs. The NEX-3 isn't technically a Micro Four Thirds camera because its sensor is larger (it uses a 1.5 crop factor compared to the 2x factor on Micro Four Thirds cameras), but since it's a mirrorless, interchangeable-lens camera of similar design, it belongs in the same group as the Panasonic and the Olympus.
The most notable difference between these cameras and the digital SLRs is the physical size. All three models are much smaller than an entry-level DSLR (and much, much smaller than midrange and professional DSLRs). If not for the protruding lenses, it would be easy to mistake any of these cameras for an overbuilt point-and-shoot camera. The next difference is the lack of a through-the-lens viewfinder. Since these cameras have no mirror, they can't include a TTL viewfinder. The G10 features an electronic viewfinder, but both the E-PL1 and NEX-3 require you to use the large LCD screens (or, in the case of the E-PL1, pay more money for a viewfinder accessory).
Olympus PEN E-PL1
upgrading to better lenses in the future, once you get comfortable with your camera. Their smaller size makes them more convenient than digital SLRs to carry around, but their smaller sensors (with the exception of the NEX-3) makes them more susceptible to noise, and the lack of a dedicated viewfinder on the E-PL1 and the NEX-3 make them awkward for traditional shooting.
While Micro Four Thirds cameras offer a lighter form factor while retaining the same exposure controls and interchangeable lenses as digital SLRs, they're not quite ready to replace a good entry-level SLR for learning how to shoot. They're bulkier, but their dedicated viewfinders are better for shooting and their larger sensors can produce slightly nicer photos.
More importantly, there's much, much more upward mobility in digital SLRs. If you play with your XS or D3000 for a year and decide you have a passion for photography, you can upgrade to a Canon 7D or a Nikon D300S. If you play with your G10 for a year and want to upgrade, you can... upgrade to a Canon 7D or a Nikon D300S. Micro Four Thirds cameras haven't yet been produced for professional work, and they've yet to be adopted by serious photographers as primary cameras. They're handy backup cameras, but for serious shooters Canon and Nikon DSLRs are still king.
Image credit: flickr users Astig!!, declencheur, Nikon USA, Canon, Sony