These three types of plays show up all the time, everywhere from readings to Broadway and they drive me crazy.
Zoo Story Clone
Usually done in short-play format.
I am one of the few people in the theatre world who is completely unimpressed by Edward Albee's ZOO STORY. The formula is simple - put two men together, have them talk and talk and then suddenly one of the men violently attacks the other. The end.
There is rarely an evening of short plays that does not include an example of this genre. I just saw another one last night at the Turnip 15 minute play festival.
Bickerfest
Similiar to Zoo Story clone but without the exciting violence at the end. And the people arguing - or rather bickering which is basically arguing about trifles - are not necessarily both men. People bickering is not drama. Few people in the theatre world get that.
Wallowing in Squalor
Writing this type of play will win you a Pulitzer, as AUGUST: OSAGE COUNTY demonstrates. Wallowing in squalor is a genre that allows wealthy upper-class theatre-goers to enjoy the misery of dysfunctional and/or poor people, who suffer and do bad things and then die, go insane or just sink down into their own filth and hopelessness. Class war as guilt-free art.