Does Casio make good digital cameras?

Or are Canon and Nikon better?
And how good is Sony?

No
now answer mine

Canon and Nikon make the best DSLR cameras.
Canon, Nikon and Sony do the best point and shoot digital cameras.

Yes, the 4 brands (including Casio) make good cameras.

Have a look at Canon PowerShot G12 Digital Camera (High Sensitivity 10 MP, 5x Zoom) 2.8 Inch Vari-angle Purecolor LCD

Premium image quality in low light using HS System with 10.0 Megapixel high-sensitivity CCD
Canon 5x (28-140 mm) lens with optical Image Stabilizer and Hybrid IS
7.0 cm (2.8 Inch) vari-angle PureColor II VA LCD with Electronic Level, and optical viewfinder
Full Manual control with Front Dial, ISO adjustment, RAW & DPP software
HD Movies (720p) with stereo sound and HDMI

Probably the Casios are good, but I would prefer to stick to the photo brands such as Nikon, Canon, Sony, Fuji, Pentax, Olympus (in no particular order).

No. Yes. Ok.

The only way you can tell is to see the results.
Personally i would stick to manufacturers that have traditionally made cameras.
Ie pentax, Nikon, Canon etc as you already know that the results will be good.
However having said that i bought a samsung wb550 and that is a great little camera so long as you are aware of its limitations.
As for casio? Well you are not going to get a top of the range compact camera but do you need a top of the range compact.
Cheaper cameras can still take good photographs and unless you are a professional photographer or a serious amateur and only want a camera for snapshot pictures then a casio is probably ok