What is established translation for "Application crash"? I routinely use simple transliteration
Крэш or 'падение программы' but that does not sound correct. What is the commonly used translation for that phrase?
It highly depends on the register you're talking/writing at.
Аварийное завершение программы is suitable for a formal register, like a technical manual. It's too wordy to be used in colloquial speech.
Падение программы should be OK in the internal docs targeted at programmers, testers etc. It should probably be OK in speech, even maybe with the users (this depends on their background).
Крэш is very slangy. Sure enough, when speaking to the fellow programmers, this can be more than suitable. However, I'd refrain from using крэш in any written docs, manuals, ticket descriptions, or whatever.