You haven't refined your definition of "good quality", and you did not specify any other requirements eg. low light capability, zoom power, size (eg. coat / pants / shirt pocket / hang around your neck like an SLR). Therefore it is rather difficult to make specific recommendations.
Nothing in the P&S world come close to the quality (optical, sensor etc) of any DSLR.
Most P&S cameras have similar sensor capability in good strong daylight and low ISO setting. In this case, the biggest different in image quality relates to the optical quality - Canon and Panasonic are the two big players here. Panasonic uses Leica (branded) lenses and are revered for the excellent tele-zoom brightness (low f number) and image quality eg. the Lumix FZ and TZ series. The biggest problem with the Pana is poorer high ISO image quality when compared to other many other major brands.
If you need good high ISO to shoot in low light, then Fuji and the new Canon P&S are good candidates.
I have always been a fan of the Fuji F series and the F30 is my casual camera. I have been tempted with the newest F70EXR / F200EXR (yes there is a new F80EXR coming as well). All major reviews out there praise the high ISO low light performance. When I do "pixel peeping" (ie. looking at the pictures at 100% size with no "shrink to fit screen) on the sample pictures, the picture detail and resolution seem to be there, with good noise suppression. However, I just cannot get used to the weird sort of "mosaic" pattern the newer high resolution (eg. 10MP+) SuperCCD make.
The biggest selling point of the Fuji camaera is good value for the PRICE. All series, from basic to advance, are significantly cheaper than brands such as Canon. IMO, the optical quality of the Canon is better than the Fuji, but not too much in everyday outdoor pictures.
Two new Canon non-DSLRs come out recently, equipped with a new high sensitivity 10MP 1/1.7" CCD. If you want small shirt-pocket size, the S90 is good to go. If you want a little bit more tele-zoom power and better optical quality, at the expense of size (shirt -> coat pocket), the G11 that Cinema Face recommended is good for you.
I do not have any of these new model cameras, but from seeing sample pictures on review sites, I prefer the high ISO pictures of the Canons to the Fujis, because the Canons have smoother texture at a slight expense of blurring sharp details. IMHO though, you have to see for yourself to decide.
I don't really care for video modes in digital cameras myself (though it may be useful for short clips in unexpected situations). I would rather get a dedicated digital camcorder for that. Therefore I did not give any consideration to this item in my comments above.