Sorry for the late reply, I wanted to be able to sit down and write something more than “yeah!”. 
All of them are usually. Though, different types of photography may address them in different ways (astrophotography vs. photojournalism for instance).
From a processing perspective I tend to break noise down into two main groups, and will approach each of them differently.
- Chroma noise
- Luminance noise
(This is not counting things like hot pixels or spurious noise that I think an impulse filter usually handles.)
Cambridge in Colour has a good page on this with a nice example image:
Image noise
That they then show as composed of those two primary components, Chroma and Luminance noise:
Chroma noise
Luminance noise
The splotches from the Chroma noise are the type of noise that I personally tend to aggressively attempt to remove.
The luminance noise usually reminds me more of film grain, so I tend to tolerate it better. (I even have a scan of film grain that I very often use over my images to add some ‘structure’ back: relevant pixls article.)
Unless it’s really, really distracting I’ll usually just leave luminance alone.