If you put 'greatest ever cult movies' or similar in a search engine you will get links to several different lists, and of course they are all based on personal opinion so it's hard to choose. But this Movie Times list is interesting because it looks at both modern and classic cult filmss. According to Movie Times, the greatest cult film of recent years is The Big Lebowski, but most lists concentrate on older movies. This is because it usually takes some years to achieve cult classic status.
Top of the 'classics' list is Blade Runner, and this movie is found in the top 10 of most cult lists. Others that come up again and again are The Rocky Horror Picture Show (my own cult favourite, for what that's worth), Night of the Living Dead and - maybe less famous globally but a perfect example of a cult film - This is Spinal Tap. So you would probably find your answer among these.