1. Sensor size
Bigger is usually better when it comes to sensor size, but it's not the whole story. More important is the ratio of pixels to sensor size. Cramming more pixels onto a smaller sensor reduces the light sensitivity - larger sensors have more room for larger pixels. There is a big difference between the compact-type sensors in small cameras and the APS-C sensors in DSLRs. Full-frame is the ideal but it's expensive.
2. Interchangeable lens
There's an old rule of thumb when it comes to DSLR that places importance on the lens quality rather than the camera body. Faster lenses let in more light, giving you more options for controlling exposure, and are less prone to distortion than all-in-one super zooms. In the end it comes down to priorities - different lenses give you creative freedom, but you need to be prepared to carry them with you.
This is another major feature you'll need to compromise on if you're looking for a small camera. The limited optical zoom on cameras like the Canon G10 (which has a 5x zoom) is one of the main drawbacks. If you're shooting outdoors at events (especially sport), you may want a bigger zoom.
4. HD Video
There are significant limitations to HD video through a photo camera, including file/time restrictions, focus and editing complications. On the upside, HD video could come in particularly handy for weddings, parties, and other social events suited to bite-size video recording. In the case of HD-capable DSLRs or Micro Four Thirds cameras, there's the added benefit of lens options, which you don't get on a consumer camcorder.
5. Size/Weight of Camera
Not everyone wants to carry a DSLR. Power zooms offer large zoom range in a slightly-smaller-than-DSLR body, while high quality compacts like the Nikon Coolpix P6000 and Olympus EP-1 offer a truly small body. The downside to smaller cameras is usually a tradeoff in terms of sensor size and image quality (though this isn't always the case, as with cameras like the Sigma DP2).
Also in this series, Stepping up to a DSLR camera
Part 3: Should you consider a power zoom instead?
Part 2: Should you consider Micro Four Thirds instead?
Part 1: The megapixel myth
Also see our Group Test of 11 Digital SLR Cameras