Not all cameras save JPEGs in the same manner, with some models using different compression algorithms than others. Most DSLRs and point-and-shoot models tend to use a decent form of compression with acceptable results, very similar to a RAW image. However, many camera phones and low-end models tend to use quick and dirty algorithms to compress their images, resulting in blocky photos with details that are difficult to discern. Keep those quality settings on max to minimize the effects as much as possible, or invest in a better camera for best results.
Grain and NoiseWhen a DSLR increases its ISO to compensate for a darker scene, there's often little visible noise in the resulting image. However, the poor light sensitivity of a smaller sensor means that even a slight increase in ISO can introduce a great deal of noise. Concert photos taken with cell phone cameras are a great example of this. If you're finding your pictures a little too grainy, try a better lit scene, or a camera designed with darker scenarios in mind.
Spots, Dots and Circles
Fuzzy, Washed-out Pictures
This is the same reason why some professional photographers debate the usefulness of filters on professional lenses, with claims that UV filters unnecessarily block light and degrade image quality. The point is, ensure you're always using good quality glass on your cameras and lenses, and avoid plastic if possible.
Images via Flickr user viking_79, mobile-review.com, and DPAnswers.