Recommendations will depend somewhat on your definition of compact or thin. As you can see above, recommendations so far range from prosumer-style cameras which are like miniature DSLRs, and certainly won't fit in a pocket, to compact big zooms that would fit in, but bulge, a pocket, and small true compacts.
I'm going to guess that you are actually meaning that you want a real slim compact camera that could fit in a chest pocket of a shirt (even if you put it in a purse...I'm just referring to the size). That's personally what I like in a compact to go with my DSLR - I figure if I'm not wanting to carry the DSLR with me, I should have something that is the complete opposite - super-small and inconspicuous - but that can still give me a decent shot when I need one, can be printed up to 8x10 at reasonable quality, and have some nice features.
So I'd recommend taking a look at the Sony W-series or T-series, the Canon SD series, the Nikon S-class slimlines, the Fuji F200, or the Panasonic FX or FS series cameras. By no means is that list exclusive of other brands - but just some of the slim, compact cameras that are truly small and pocketable and can still give you some nice shots.
I bought a Sony T100 a few years ago which has been the perfect companion for my DSLR - it's a credit-card style slim camera with an internal zooming lens that does not extend outside the body, it has a sliding cover over the lens making it well protected, and has some decent features like a thirds grid, spot meter, image stabilization, 5x zoom, a big bright LCD, and a battery that lasts forever.
Brands don't really matter for much anymore - check out the cameras and see if they suit the size requirements you are looking for, then make sure you can find a comfortable way to hold and shoot with them. Then you can shop prices and features to decide on the camera for you.
