Fast treewidth algorithms
As far as I know, the state of the art is what is reported in

Hans L. Bodlaender, Fedor V. Fomin, Arie M. C. A. Koster, Dieter Kratsch, and Dimitrios M. Thilikos (2012), "On exact algorithms for treewidth", ACM Transactions on Algorithms 9 (1): A12, doi:10.1145/2390176.2390188.

The methods described there include an implemented $O^*(2^n)$ algorithm with some heuristic optimizations to make it faster in practice.