" I don't mean that in the sense of photography as a hobby or a profession, but simply as a method for taking images — of friends, family, and projects — that actually look good." Reading that, I do not think you should buy a D-SLRs at this point. I have a Canon Powershot SX20 IS and I have handled a few D-SLRs belonging to my friends.
1. D-SLRs are quite bulky - You can't walk into every party/gathering with a D-SLR. I have receive comments like "Oh! What's that? A camera ?! " And of course you can't move around easily, leaving it somewhere - It will always be on you.
2. D-SLRs can be tricky. It will take some time for you to learn all the settings - and would you really have the time to to mess with all this while things happen around you ? (I remember an incident - I changed to a telephoto lens on a Nikon at an event as the stage was far and the normal lens wouldn't zoom so much. Then my friend suddenly started serenading his wife nearby and of course I missed capturing the moment properly - telephoto lens won't take the best closeups.
3. D-SLRs usually need more than one lens (you will need to buy a telephoto lens, then perhaps a macro lens as you go along). And lenses don't come cheap.
I am an amateur photographer and I own a Canon Powershot SX20 IS, bought a year back. The major reasons: Less bulky than D-SLR, Super-macro mode( minimum focusing distance of 0 cm! ), 20X zoom, my confidence that I won't have the patience to change the lens to suit the scene, my confidence that I won't invest in extra expensive lenses. Being a little flighty, it is well suited to taking shots of whatever I feel like - sometimes it's a bird in the sky, the very next moment a beetle crawling in the grass; and it does have manual mode in case I ever have the leisure of setting each parameter on my own.
To tell the truth, this Powershot is still bulky (it might not have a heavy lens, but it is 0.500 Kg, so almost as much as an entry level D-SLR) but I tolerate it for the great zoom and super macro capabilities in one lens.Frequently, my photos have been mistaken for D-SLR shots - so it depends on the photographer and the post-processing software too. Few photos I took recently with a borrowed Nikon D-SLR came out so well that I almost wished that I had bought it instead, but then I remembered the weight, the pain of adjusting exposure, aperture,etc and that these couple of good photo came from a bunch of twenty bad ones.
I suggest you go for a decent P&S - I've seen photos taken with a Canon IXUS and they look pretty good. (Try out in the stores which zoom capability you need). Perhaps you could borrow a friend's D-SLR for a month (yes that long!) and see if it suits you. Since you have only used mobile cameras till now, maybe you will be happy with the quality of P&S photos. I still believe it is a good idea to start with a simple camera so you learn from all the bad photos you take - and then when you are sure it isn't your ability but the camera's limitations that are restricting you from taking better photos (you start complaining about exposure or ISO range), go for the D-SLR !