Taxonomy of notable regular expression automata
Watson (Tech. Rep. Univ. Eindhoven 1995) has written a taxonomy of finite automata construction algorithms; a few more recent developments are found below. 

For NFAs with epsilon-transitions, the parsing theory book by Sippu/Soisalon-Soininen (Springer, 1998) contains a variant of Thompson's construction. Ilie and Yu (I&amp;C 2003) and Gulan and Fernau (FSTTCS 2008) give refined versions of the classical construction. The minimum required size of epsilon-NFAs corresponding to regular expressions is further studied by Gruber and Gulan (LATA 2010). The structure of the underlying digraphs resulting from Thompson's construction is studied by Giammarresi, Ponty, Wood &amp; Ziadi (Discr. Appl. Math 2004) and by Gulan (Tech. Rep. Univ. Trier, 2010).

Regarding epsilon-free NFAs, I want to mention the earlier work by Berry &amp; Sethi (TCS 1986) and by Brüggemann-Klein (TCS 1993), but that is probably covered by Watson's taxonomy. 

Hagenah and Muscholl (RAIRO 2000) give a fast parallel version of Hromkovic, Seibert &amp; Wilke's (HSW) algorithm. The initial lower bound on size (number of transitions) of epsilon-free NFAs by HSW is improved by Lifshits (IPL 2003). Geffert (JCSS 2003) improves the upper bound in the case of binary alphabets; Later Schnitger (STACS 2006) improves the lower bound on the size of epsilon-free NFAs (for largely growing alphabet sizes, the algorithm by HSW produces asymptotically optimal NFAs), and shows that size $n\cdot 2^{O(\log^*n)}$ suffices for binary alphabets.

Also note: Regarding fast algorithms for regular expression matching, I am aware of recent work by Bille and Thorup (ICALP 2009, SODA 2010). They use the classical Thompson construction (plus of course many tricks for getting speed).