The limited sensor and lens size of a smartphone's camera places a limit on image quality. That said, most people only take small images for FaceBook, Instagram or the phone's screen - most smartphones are more than enough for such tasks. While generally good enough, image quality varies a lot and perhaps the worst measure is pixel count - the number of megapixels.
Here is a camera comparison test of one of the most popular smartphones and another that aces the megapixel race. Having played with both cameras I'm not terribly surprised.
A bottom line is that if photography is important to you, get a dedicated camera. A $200 point and shoot will run rings around any smartphone camera and the difference is astonishing if you move above $500.
That said - having a camera everywhere you go is a feature.