Did early Christians believe the world was about to end? Truly I say to you, there are some of those who are standing here who
  will not taste death until they see the Son of Man coming in His
  kingdom. (Matthew 16:28, NIV)


Edit: adding another verse in order to make sense of the answer linked below.


  Truly I tell you, this generation will certainly not pass away until
  all these things have happened. (Mark 13:30, NIV)


End of edit

One interpretation of this is that Jesus believed the end of the world would happen within a few decades. If that's what Jesus meant, was it a new suggestion or were there precedents? What evidence is there that Christians in the first century subscribed to this belief?

Other interpretations have been suggested, like the ones summarised in this answer:

https://christianity.stackexchange.com/a/4310/45084

What are the earliest sources we have for such interpretations?

What sources show us how ideas about the apocalypse changed over the course of the first hundred years or so of Christianity?

I'd sort of expect there to have been a big crisis in the religion when it started to become clear that the first generation was all dead and the end of the world hadn't come, but as far as I can gather that didn't really happen. There were new sects and theological disputes as the faith spread, but the date of the apocalypse doesn't seem to have been a central factor. Is that right?
The text you link to, Matthew 16:28, is so very closely linked to the next verse, '... and after six days' that its natural interpretation is that the those present actually saw the coming of the Son of man on the mount of transfiguration and that Jesus' words relate to that experience, not to the end of the world.

But it is evident that the early church viewed the return of Christ as immediate. That is to say, as imminent in their own, personal apprehension.

Paul says to Titus :


  ... the grace of God that bringeth salvation ... looking for that blessed hope and the glorious appearing of the Great God and our Saviour, Jesus Christ. [Titus 2: 11, 13 KJV.]


The urgency and immediacy of the expectation was a hope and a desire. Faith looked in hope for the coming of the Lord Jesus. Love longed to see him as he really is, either again or for the first time.

The women who went to the tomb went there in love, to anoint the body of Jesus. Mary was bereft without him, longing just to find his deceased body, frustrated because someone appeared to have stolen him, John 20:15. 

After his ascension, the disciples had to be exhorted to activity by no less than angels as they were standing around looking at the spot in the sky into which Jesus had disappeared, Acts 1:10 and 11.

Paul had to exhort some of the Thessalonians that if a man will not work neither let him eat as it appears some had given up working because of the imminence of the Lord returning and the world ending. Paul had to remonstrate with them that it was irresponsible to respond in that way, II Thessalonians 3 : 6-15.

At the end of his life, Paul exhorts Timothy :


  Henceforth there is laid up for me a crown of righteousness which the Lord, the righteous judge, shall give me at that day : and not to me only, but unto all them also that love his appearing, [II Timothy 4: 8 KJV.]


It was love that prompted the early church to look for the appearing of the Lord.

Towards the end of that era, as scripture closed, John the apostle, aged then between ninety and more than an hundred years old - at the very end of his Revelation and at the close of the first century, writes :


  Surely I come quickly. Amen. Even so, come quickly, Lord Jesus. [Revelation 22:20 KJV.]


Yes, I see that "early Christians viewed the end of the world as imminent". And I believe that the bible itself as a "source" demonstrates that views about the apocalypse did not change at all during the first century.

For further generations, faith and love and hope should be unchanged, despite the passage of time, despite the passing generations. For with the Lord, a day is as a thousand years, and just a couple of days have passed since he ascended. And the Lord is not slack concerning his promise, II Peter 3:8.

Faith and hope and love still gaze upwards, imminently expecting the return of the Lord Jesus.