A comic classic must be re-readable, must be read spontaneously (and not prescribed in courses), and must be not only enjoyable but also funny on re-reading.
The best comic work generates a kind of 'depth' from the world it creates - this world must be delightful.
Farce is not comic - because it is heartless.
But in the lists below this category excludes 'great' literature which is also comic - to get onto the list the work must primarily be comic (although almost never exclusively comic).
Best comic novel: Lucky Jim by Kingsley Amis.
Best comic travelogue: Three Men in a Boat by Jerome K Jerome
Best comic novelist: PG Wodehouse, especially Jeeves stories
Best writer of comic verse: Lewis Carroll
Best writer of comic poetry: John Betjeman
Best comic playwright: Tom Stoppard (early)
Best comic 'diary': Diary of a Nobody by George and Wheedon Grossmith