(There is a newer answer to this question.)
I’m often asked that question, and I have a short answer. The Canon G11. It gets good reviews (at a site where you can trust the reviewers), it has great optics, it takes video, it shoots RAW, and it allows the user creative control but can still function effectively on full auto. And you get all that in a portable unit that doesn’t require any accessories.
While I consider the G11 a sweet spot when it comes to price, performance, and portability, I understand that there are numerous other factors that go into choosing a camera. The G11 gives us a place to start, but it may not be the right choice. There are many great cameras available for less than $400, if price is an issue. There are also many point-and-shoot cameras that are smaller.
On the other hand, maybe the delay when you press the shutter release on your point-and-shoot has resulted in too many lost shots. Or perhaps you’re looking to take even more creative control of your photos. In that case, it may be time to consider a digital SLR.