Early 20th century communist/socialist authors in the West, such as Upton Sinclair and John Steinbeck, speak admiringly of the Soviet Union in their writings. The earliest major socialist detractor I can think of was Orwell, but his anti-Soviet views didn't seem to have gotten much traction in Western communist circles. Even today many communists downplay Soviet failures, but even so very few would claim to be proponents of its system. So when did most Western communists really begin to turn on the Soviet Union and other communist states?
There were, over the course of the 20th century, a series of breaks Western socialists and communists made with Soviet leadership. The first was during the initial October Revolution; a sizable contingent of the 2nd International disagreed with the Bolsheviks; these reformists wanted to try and implement socialism via western parliamentary democracy rather than engage in violent revolution. This inter-leftist dispute reached its head in Germany in 1919 when the SPD (the German socialist party) refused to support a revolution led by its own (current and former) radical elements and instead crushed revolutionary leftists in co-operation with the Freikorps, a far-right militia whose members would go on to form much of the core of the Nazi leadership and paramilitary forces.
The second major break comes in the 30's, with Leon Trotsky's exile and Stalin's rise to power and subsequent purges of the army and Party. While not all those opposed to Stalin's actions were "Trotskyists", his writings on what he perceived to be the failings of the Soviet Union influenced many Western critics, including Orwell. Animal Farm reads like a kid's version of Trotsky's "The Revolution Betrayed" as a matter of fact.
The third major break happened in 1956, with the Soviet invasion of Hungary. This caused an uproar in Western leftist circles, most notably in Britain, where the Communist Part of Great Britain was crippled after most of its celebrated members (including incredibly influential historian E.P. Thompson) left in protest of the Soviet intervention. Those that remained in the CPGB were labeled as "Tankies", as they supported "rolling in the tanks". This remains to this day an insult used against Marxist-Leninists in leftist circles.
The fourth break occurs in 1968, over the Soviet intervention in Czechoslovakia. This would lead to many Western communist parties distancing themselves from the Soviet Union and Soviet ideological dogma, instead creating a new "Eurocommunism". This was adopted by the Spanish and Italian (but notably not French, who remained ardent loyalists) Communist parties, as well as to some extent the Japanese Communist parties. All three had a great deal of electoral success in the 70s and 80s; the PCI was the largest party in Italy but was unable to form a government due to a Cordon Sanitaire put on it by the other parties.
Additionally, some Western leftists dismayed by what they viewed as Soviet "revisionism", turned towards China, which became an ideological and geopolitical opponent of the Soviet Union in the back half of the 20th century. This I know less about, however, and is perhaps better answered by someone else.