Many websites use the phrase 'Forgot password?' when prompting users to renew their login passwords. Is this correct usage or should it be 'Forgotten password?'.
Both are acceptable depending on the context.
"Forgot password" could simply be an informal (shortened) way of saying "I forgot my password." We commonly miss out pronouns to be succinct. In this case, the words form a statement.
Similarly, "Forgot password" could be a shortened form of the question "Have you forgotten your password?".
"Forgotten password" uses the gerundive (Attributive Verb), and thus is also perfectly fine, in that the page is directing the user to their forgotten password. Here, the words form a noun phrase.
This is short for "You forgot your password?" which is simple past which specifies something that happened at a specific time in the past, namely, right when you came to the site, it was then that you "realized you forgot your password".
This is short for "Have you forgotten your password?" which is present perfect which means starting at some point in the past and continuing up to and including the present.
So technically the second is correct if you are describing the psychological act of forgetting. But it sounds odd since the question is really asking, "Did you just try to remember your password and you forgot it at that moment?"
So my vote is for "Forgot your password?
Yep! By itself, without other context, ("forgotten password"), I'd be reading "forgotten" as a participle (a verb form used as an adjective, describing the noun "password"). reference: more participle info.
In a different context ("Have you forgotten your password?"), the same word becomes part of the verb phrase ("have forgotten"), which tells what the "you" did. No longer does it describe "password"; now "Have...forgotten" is the verb (what you did), and "password" is the direct object of that verb (the thing you forgot). reference: more direct object info.