Digital Photography Review has published a comprehensive guide to the new category of cameras, sometimes called Mirrorless Cameras and other times called Mirrorless Interchangeable Lens Cameras. Instead of old school SLRs, let's call them MIL's. There is more than one format in this category, but the standout format is the Micro 4/3 format used by Olympus and Panasonic. DP breaks out the different categories of cameras within this loose camera definition with Beginner, Intermediate, Enthusiast, and Specialist varieties.
For people looking for a professional alternative to DSLR's, the Enthusiast and Specialist sections are a great place to start. For myself, I must admit that some of these cameras are quite intriguing. I've been very impressed with the Panasonic DMC-GH2 and the Olympus PEN E-P3, and the Nikon 1 V1 is about the cutest camera I've had in my hands in quite a while and it feels extremely well-made. Though I've been a loyal Canon user for many years, that V1 is really tempting. And the Sony NEX-7 sports a 24 MP sensor and appears to be at the top of the image quality heap at the moment. Lots of people are singing its praises.
The other place for these cameras is as a back-up or casual camera; those cameras we like to take with us all the time or when it isn't practical to carry around a full SLR system. They offer enough control and image quality that when we make an image, we know we won't look at it later and wish we had used something different. There's a lot to be said for that. Anyway, check out the article here.