Regular expressions without alternation
The class of regular languages that can be described by regular expressions without union (and without complementation) are known as union-free regular (also: star-dot regular) languages. This class of languages apparently has received some attention recently:

Benedek Nagy: "Union-free regular languages and 1-cycle-free-path-automata", Publicationes Mathematicae 68(1-2), 2006.

Sergey Afonin and Denis Golomazov: "Minimal Union-Free Decompositions of Regular Languages", Language and Automata Theory and Applications, Springer 2009. 

Galina Jirásková and Tomás Masopust: "Complexity in Union-Free Regular Languages", Developments in Language Theory, Springer 2010.