What is standard coordinates? What is meant by the word standard in "Euclidean space is special in having a standard set of global coordinates."?
Then "A manifold in general does not have standard coordinates"
This makes me think standard means something else then 'most common used'.
Is R^n special in any sense, as a manifold?
This is from Loring W. Tu - Introduction to manifolds

Usually when we write "$\mathbb{R}^n$" we are thinking of an explicit description of it as $n$-tuples of real numbers. This description "is" the standard set of global coordinates, namely the coordinate functions $x_i$. But this description isn't part of $\mathbb{R}^n$ "as a manifold", in that it contains more information than just the diffeomorphism type of this manifold. What I mean by this is that if I give you an abstract manifold which is diffeomorphic to $\mathbb{R}^n$ -- but I don't tell you an explicit diffeomorphism -- then there isn't a "standard" set of coordinates for it. And if you have a manifold which isn't diffeomorphic to any $\mathbb{R}^n$, then there is no set of global coordinates for it (otherwise you could use those coordinates to produce a diffeomorphism to $\mathbb{R}^n$).  
