This concept is usually called biorderability (there is also left- and right-orderability).  There are many examples, such as free groups and surface groups.  Most spectacularly, the pure braid groups are biorderable, while the full braid groups are left orderable but not biorderable.  The left ordering on the braid groups is usually attributed to Dehornoy, though it was discovered even earlier by Thurston (but not published).

Dale Rolfsen has several nice surveys of material related to this on his webpage <a href="http://www.math.ubc.ca/~rolfsen/reprints.html">here</a>.  In particular, there is the complete text of a nice book called "Why are braids orderable?" that he wrote with Patrick Dehornoy, Ivan Dynnikov, and Bert Wiest.  I believe that a new and much expanded edition of this book was just published.