For non-Russian-speakers it might be not so easy to detect the difference between words that are almost synonyms; for instance the difference between "теперь" и "сейчас" (cf. this question).
When would you use "опять", when "еще раз" and when "снова"? (assuming, of course, that I'm not wrong and they are indeed (almost) synonyms)
The answer by Netch is wrong.
"Еще раз" "one more time" is used when you expect that the event happens or will happen for the last time, you do not expect it to repeat again.
"Опять" and "снова" are used for actions that you expect to repeat again and again.
"Опять" is usually used for undesirable events.
Опять придется его об этом просить.
I do not want to irritate him with my request again but I have no other choice.
Ничего страшного, я снова его об этом попрошу.
Nothing bad, I can ask him again and he will do it without negative reaction.
Я попрошу его об этом еще раз.
I will ask him again one more time (I hope it will be the last time).
Also "снова" may refer to starting anew a prolonged action, while "опять" may mean a continuation of the previous action.
Он снова начал готовиться к экзаменам
Possibly a year passed from the last time and he chose another university so he started to prepare anew.
Он опять начал готовиться к экзаменам
Probably something interrupted his preparations for a day or two and now he continued the preparations.
Он решил построить дом снова
He decided to build a house anew in place of his previous house that was destroyed.
Он опять решил построить дом
He again decided to build a house (he already decided so previously but changed his mind).
In short, "опять" is used when you want to underline the unavoidable repetitiveness of the event:
"опять начались дожди", "опять я заболел", "опять крысы испортили продукты", "он опять стал принимать наркотики"
"Снова" is used when you want to underline that the event starts anew and the results of the previous event are lost or that the event gained new momentum:
"придется снова собирать все документы", "он снова влюбился и снова приобрел интерес к жизни", "после выхода из тюрьмы он снова начал строить свою карьеру".
oпять only applies for undesirable things, right? It would be then absurd to say e.g. она опять получила Нобелевскую премию?
Not from dictionaries, but from persional experience:
Ещё раз is mainly used when somebody asks to do something in a future, while опять and снова are preferred for finished actions.
Ты должен позвонить ему ещё раз.
Then, снова is used for intentional actions, but опять for occasional (unexpected) ones, even in future. There is phrase which expresses that the action was intentional:
Не «опять», а «снова»!
"Ещё раз" may be used for past events to put accent on repetition:
Он ещё раз сходил за ёлкой, потом ещё раз... (["Падал прошлогодний снег"])
The boundaries between these meanings aren't strict and depend on speaker.
