Though the CIA distributed it, it was not really what you'd call secret. It was read out to meetings around the USSR within weeks. The reaction varied: in Stalin's home Georgia, there were angry demonstrations. Party stalwarts were insulted by the critique of Stalin's war leadership, called for Krushchev to be replaced by someone like Molotov. The students, intellectuals were aghast at the report but saw it as a good sign that such things could be publicly admitted. In the new Eastern Bloc, it seemed to remove a threat of Stalin-like repression, and created an upheaval, especially in Poland ( when the premier Bierut had a heart attack reading it) and it certainly sparked the Hungarian revolt. The Soviets had already help crush strikes and protests in the GDR in 1953, and likely the Speech further influenced the government there to split off a special army unit for internal actions in 1956, the Volkspolizei-Bereitschaften.

Sino-Soviet relations certainly suffered: it's not my field, though, so I can't say how much was ideology and how much was an inherited border dispute. Certainly, as Mao began pushing into the intense collectivization of the country in the Great Leap Forward almost immediately afterwards, the last thing he would have acknowledged was that such drastic authoritarian actions could be mistaken, and open to question. And the essence of the speech was just that.

Fitzpatrick: On Stalin's Team