The comments by users of this dictionary suggest that many people who are interested in the meaning of the word abide are motivated by one of two rather distinct things: the Bible, in which, for instance, Jesus calls upon his followers to "abide in me"; and the movie The Big Lebowski, in which Jeffrey Lebowski (aka "The Dude") proclaims that "The Dude abides." Both the movie and the book have done much to keep the word in general current usage. Though the sources are wildly different, in each of these particular examples, abide is used as it is defined at the first intransitive sense: "to remain stable or fixed in a state." In the phrase "abide in me," Jesus is asking his followers to stay constant in their relationship to him. The exact meaning of "The Dude abides" is a topic of some debate, but clearly there is some notion of the constancy of Lebowski himself—metaphysically perhaps—being asserted.
Although the phrase can’t abide has for some the feeling of a modern colloquialism, it has been pointed out that such use dates back at least as far as Shakespeare: in Henry IV, Part II, Falstaff says “she would always say she could not abide Master Shallow.”