Status of Cerny Conjecture?
Trakhtman has a bibliography on the problem, which is apparently kept up to date; so I suppose Černý's question remains unresolved until today. The same is stated in Volkov's recent survey (LATA 2008) linked from the wikipedia article cited in the question. There you find pointers to some partial results, for example, for which subclasses of regular languages the conjecture is known to be true. Even more recent is a research paper by Ananichev, Gusev &amp; Volkov (MFCS 2010) on a related topic, where they confirm that Černý's conjecture is still open now (at least as of May 2010).