TITLE: Does Vitali construction exhaust non-measurable sets?
QUESTION [18 upvotes]: We can construct Vitali type of non-measurable sets. But is this the only type of non-measurable sets? That is, are there any other non-measurable sets constructed from a different approach?
Please provide some answers or references. 
Thanks.

REPLY [7 votes]: John C. Oxtoby's "Measure and Category" has a chapter on non-measurable sets.  He covers the following three examples of non-measurable sets:

Vitali sets (group-theoretic)
Bernstein sets (topological)
A construction due to Ulam (set-theoretic)