As for the sensor size I think its no more a definite indicator of quality than pixel number (obviously they do pay a part but you can't just judge on a singe number) and when it comes to aperture I can stop my compact to f2- maybe not noctilux levels of separation but its okay for me right now.
The depth of field is not determined by the aperture alone: f/2 on a compact P&S will have a much, much, much larger depth of field than f/2 on a full frame dslr. On a Canon S90, if we pretend that the largest aperture at 50 mm equivalent focal length (~ 10.7 mm) is f/2, then at a subject distance of 2 m, you have a depth of field of 85 cm! If you use a 50 mm lens at f/2 on a full frame camera, your depth of field is 19 cm.
Hence, you don't nearly have as much creative freedom with a P&S than with a dslr or some other camera with a large sensor.
I think the point I was making is that there is a huge range of cameras out there which shouldn't be reduced to a "crappy p&s" / DSLR dyad, and if the OP was after taking a lot more photographs then a compact may well be worth having a look at (I know that I wouldn't have taken nearly as many photographs if I'd have gone down the DSLR route at this stage and while I will move on up in the future my compact will always have a place in my pocket!)
If someone wants to learn photography, for two reasons, I think point and shoot cameras are not a good tool: (1) You don't have a proper viewfinder. (2) Your creative freedom is very much limited.
I'm not saying you cannot take good pictures with a point and shoot or that it's impossible to learn how to take good pictures with a compact camera, not at all. And to most people, a dslr is not just overkill, but the wrong camera which gets left at home, because it's too heavy/complicated. However, if you're looking for a new camera for the express purpose of learning the basics of photography, my advice is to go for a dslr instead of a point and shoot, that's all.
For the record, I also happen to have a `compact,' a Sigma DP-1 which I do take with me whenever I want to/have to leave my dslr at home.