(I'm sure 99% of the people reading this knows what this means, but in this comment I'm using "eschatological" as the adjective to describe teachings that proclaimed/predicted what is more-or-less the "end of the world"; and I'm using "eschaton" as the noun form of this event.)
There was a little mini-movement that had in heyday in the 1990s (and a bit before that) that really tried to dissociate the historical Jesus from any sort of true end-of-the-world type teachings, and instead ascribed these to later Christians who then simply placed them back on the lips of Jesus in the gospels. But as of 2015, this idea is virtually dead in the water. This shift partially had to do with the decline of the idea that certain non-eschatological sources were very early or in fact represented the most primitive sources which (more) faithfully captured the teachings of the "true" historical Jesus -- sources that are now later and secondary.
In its wake, we can now find comments like those of Dale Allison, who goes as far as to suggest that
sober recognition of Jesus' eschatological orientation is perhaps the chief accomplishment, if it has any, of the quest for the historical Jesus. Whatever else he may have been, Jesus was, as Schweitzer insisted, an eschatological prophet.
We have classic statements of Jesus in the earliest gospel to the effect that "there are some standing here who will not taste death until they see that the kingdom of God has come with power" and "this generation will not pass away until all these things have taken place." The latter statement here follows a discourse that focused on various "eschatological things," like "they will see the Son of Man coming in clouds with great power and glory; then he will send out the angels, and gather his elect from the four winds, from the ends of the earth to the ends of heaven."
It's also instructive that the apostle Paul, whose epistles were written somewhere roughly between the years 50-60 CE, also shares this imminent-eschaton view. In his first epistle to the Thessalonians -- widely held to be one of the most primitive Christian documents we have -- we see an even earlier reflection which conforms closely to the later gospel portrait of Jesus' expectations:
the Lord himself, with a cry of command, with the archangel's call and with the sound of God's trumpet, will descend from heaven, and the dead in Christ will rise first. Then we who are alive, who are left, will be caught up in the clouds together with them to meet the Lord in the air; and so we will be with the Lord forever.
Further, in his first epistle to the Corinthians, he describes the eschatological resurrection of all:
We will not all sleep/die, but we will all be changed, in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised imperishable, and we will be changed.
It's interesting that in these passages, Paul speaks of "we who are alive" and "we will be changed." If you look at the context of the latter, it seems that Paul is making a distinction between the dead, who will be "raised," and the living -- the latter of whom Paul seems to group himself with -- who will (only) be changed; suggesting that he expected to be alive when the eschaton dawned. (This interpretation may be even more likely when we look at a textual variant in the manuscripts of 1 Corinthians here. Well, actually there are several variants: e.g. some that change "we will not all sleep/die" to "we all will sleep/die." Philip Comfort, commenting on these variants, suggests that 'since Paul himself died, some scribe may have thought it necessary to make an adjustment to the text "we all will sleep, but we all will not be changed" . . . This could be interpreted to mean that all human beings will die but only Christians will be transformed.')
I should mention that there is some debate over what exactly will happen at the eschaton. I mentioned the eschatological discourse of Mark 13, ending with "this generation will not pass away until all these things have taken place." Although there's less ambiguity with things like "they will see the Son of Man coming in clouds with great power and glory; then he will send out the angels, and gather his elect from the four winds, from the ends of the earth to the ends of heaven," some have wondered whether the other things in the larger eschatological discourse here were meant literally, or if they were just some of standard apocalyptic hyperbole that might ultimately be hinting at more mundane terrestrial events. For example, Mark 13:24-25 reads
in those days, after that suffering, the sun will be darkened, and the moon will not give its light, and the stars will be falling from heaven, and the powers in the heavens will be shaken.
Did they actually expect literal stars falling or a literal darkening of the sun, etc.?
Those scholars like N.T. Wright often see this language as hyperbole referring, for example, the destruction of Jerusalem in 70 CE. And while it's true that there are other Jewish texts which cast earthly events in this sort of cosmic language, this strikes one as all-too-convenient: Jesus is relieved of the burden of having made a prediction which turned out to not be true. (Also, it's a bit harder to explain the "Son of Man" coming from heaven to "gather his elect from the four winds," considering that other New Testament texts seem to conceive of this as a literal event.)
But there are other reasons to not throw out the literal interpretation. Dale Allison writes
Why . . . suppose that Mark 13:24 is less prosaic than, let us say, 1 Enoch 70:6, which foretells that one day the stars "will change their courses and their activities, and will not appear at the times which have been prescribed for them," or that it is less realistic than Barnabas 15:8, which says that when the Son of God abolishes the time of the lawless one, God "will change the sun and the moon and the stars" or than Lucan's Pharsalia 1.72-80, which envisions stars plunging into the sea at history's end? According to Seneca (Natural Questions 3.29), Berossus, the Babylonian astrologer, foretold that "the world will burn when all the planets that now move in different courses come together in Cancer, so that they all stand in a straight line in the same sign." If this is not metaphor, can we be confident that Mark 13:24 is? Should we not understand Mark 13:24 the same way we understand Sibylline Oracles 2:200-202 ("But the heavenly luminaries will crash together, also into an utterly desolate form. For all the stars will fall together on the sea"), that is, literally? One wants to ask how Mark, if he had wished to forecast an astronomical disaster, could have forecast it. What more could he have said?