Question: If you are playing in the Key C major, a chord progression can be as simple as C-F-G7-C or C-Am-F-G7-C.

What are the principles while using chords like Am7,Am6, Cdim7,Csus4,Cdom9,C13,Bflat,Aflat etc (many more which I have not written). When do you use these types of chord in the C major key? What are the guiding principles in the chord progression when these chords are also used in C major?

Answer: 
One of many reasons is that the melody line contains some of the notes that occur in the particular chord, especially notes on the 1st and 3rd beats (in 4/4 time). Generally an underlying chord reflects the notes in the melody at that point. As Bob says, a lot of the examples are not strictly within the C major framework, so there could be many more answers.
Those are often just notes add to chords to give a musical piece depth. Jazz players sometimes talk about coloring chords in with added sevenths and ninths.

Am7
This is just a chord with a seventh added. Regular solution of seventh should apply with these chords as well.

Am6 
Chords with sixths are usually passing chords where the sixth acts as middle man between two notes.

Cdim7
This is a chord commonly found when a seventh is added to the leading tone chord. The seventh is flattened and still has to resolve.