What is the state-of-the-art algorithm for multiple sequence alignment?
My Vote goes to Mafft(insi) as it have ~86% accuracy and results in ~1.2 hour. Though fastest will be kalign takes only ~3 minutes to finish with an accuracy of 74.3%. 

For testing:


  For each of the 218 reference alignments in the benchmark, we applied
  eight alignment programs, resulting in a total of 1744 automatically
  constructed MSAs. The overall quality of these automatic alignments
  was measured using the Column Score (CS) described in Methods.



FIGURE 1: Overall alignment performance for each of the MSA programs tested.

(A) Overall Accuracy 

(B) Total run time for constructing all alignments (a log10 scale is used for display purposes).

doi:10.1371/journal.pone.0018093.g003

Compared Tools

http://www.plosone.org/article/fetchObject.action?uri=info:doi/10.1371/journal.pone.0018093.t001&amp;representation=PNG_L

Source and Photo Credits: 

A Comprehensive Benchmark Study of Multiple Sequence Alignment Methods: Current Challenges and Future Perspectives 

PS: This is from an old paper of 2011. If you want the new statistics you can always test on your own, by the process described in the source paper.