1) When fictional characters of any medium face dilemmas of the romantic variety (ie. forbidden love, unrequited love, etc).
2) Characters make a shitstorm out of romance issues/ non-issues, most of which could be solved be actually talking to the other person.
"Oh no, unrequited love broke up with best friend, but I can't ask out unrequited love without ruining friendship with best friend! Romangst!"
"Forbidden lover and I are in love and we banged last night, but lover is still going to get married to the bland fiance! And now my ex wishes to reunite with me and ex is still very attractive! Romangst!"
Most Shakespeare plays. See: Much Ado About Nothing, Midsummer Nights Dream, Romeo & Juliet, etc.
Most shojo manga; some shonen manga (Good example: Boys Over Flowers. So much romangsting.)