Paging /u/TenMinuteHistory! Would you mind weighing in since your flair states you study the Soviet Union?

Well, I know only about Mao, who was horrified and really regarded Khrushchev as betraying global communism. This tension between Mao and Khrushchev only got worse and it eventually led to a complete breakdown in sino-soviet relations.

Most of this comes from Judt's "Postwar" and Zubok &Pleshakov's "Inside the Kremlin's Cold War"

The main thrust of the Secret Speech was that Stalin's main crime, or "perversion" as it's called in the speech, was his cult of the personality. By emphasizing that aspect of Stalin's rule, as opposed to the Purges or the GULAG, Khrushchev was able to distance the CPSU leadership from Stalin's crimes without blaming the whole system. Mao's problem with this was that his own cult of the personality was just coming into its own in the wake of the Korean War. Thus, as long as Stalin was alive, the USSR and the PRC could "speak the same language" (to borrow from Zubok/Pleshakov). Once Khrushchev declared a cult of the personality as being inherently anti-communist, the two major states had series rhetorical issues, in addition to their growing geo-political differences.

Moving to Yugoslavia, Tito was predictably pleased with the new Anti-Stalin rhetoric. He would eventually make a return trip to Moscow in the 60's, I believe, to emphasis some kind of reconciliation. Not that anything too substantive came out of it.

As for the Satellite States, from what all I've read it seems hard to pin down exactly what effect the Secret Speech had on the disruptions that would happen later in 1956. Tony Judt seems to suggest that some of the Polish and Hungarian Party membership seem to take the Secret Speech as a sign that control from Moscow would loosen (which wasn't the case). Thus, mistakenly emboldened, agitation began which would lead to the crackdown in Hungary and a near miss in Poland. But, personally I've never read (or don't remember reading) any kind of smoking gun document from Golmuka or Nagy.