What is the latest possible time that the First World War could happen? My guess would be that at the VERY latest it would have to had happen by the early 1920s, and even that's stretching it.
EDIT: Oops. Is it possible to move move this to After 1900?
With everything being equal, it would.
But say there is someone there in the late 1880s who can change the system of alliances so that international tensions only lead to regional wars like the Balkan wars and mayor crises are avoided. Some second Bismarck or de Metternich.
My personal favourite diversion would be Nicholas, the eldest son of tsar Alexander II would not be injured in a gymnastics session, not getting tuberculosis on the brain, and not die aged 21. According to his tutors (one of them being Stroganoff the co author of the constitution singed by Alexander II days before he was assassinated) he was a VERY clever young man, I think clever enough not to conclude that the assassination of his father was proof of the need to stop reforms but the need to improve safety measures on the royal family and, on the same time, continue reforming. He was looking forward to the 20th century and was looking westward to Europe. He could probably prevent international relations from overheating in that period.
With this change of history, the drama of WWI could well have been avoided.
Perhaps this was a little bit off topic. Sorry for that. But with a little help from events late 19th century I believe WWI was not all that inevitable.