When were each of our "ultimate fate of the universe" theories widely accepted? I'm trying to piece together a sort of timeline for the prevailing "ultimate fate of the universe" theories, specifically from the dawn of the twentieth century through today. 
I know the Big Bang theory has its origins in the 20s and Hubble made his famous observations that contributed to the idea prior to 1950... but when did heat death become the accepted end theory? What was the theory before that? How many times did we switch prevailing theories between 1900 and today? Was the big crunch ever widely accepted? When?
I'm not interested in the technical explanations of each theory, just kind of when they were popular.
 A: The heat death is older than 20th century cosmology. It showed up as thermodynamics became a science in the 19th century and quickly led to the conclusion that free energy was running out. Most Victorian scientists expected that if the universe were to last indefinitely this had to be the end, but the view was not universal. Lord Kelvin argued in 1862 that this was not a problem due to the infinite size of the universe:

"The result would inevitably be a state of universal rest and death,
  if the universe were ﬁnite and left to obey existing laws. But it is
  impossible to conceive a limit to the extent of matter in the
  universe; and therefore science points rather to an endless progress,
  through an endless space, of action involving the transformation of
  potential energy into palpable motion and hence into heat, than to a
  single ﬁnite mechanism, running down like a clock, and stopping for
  ever." (William Thomson. Physical considerations regarding the
  possible age of the sun’s heat. Macmillan’s Mag., 5:388–393, 1862.)

Steady-state cosmologies hung around as a possibility for a long while: Einstein's original cosmology was one, and Hoyle famously championed one that was both expanding and infinitely old. They lost out due to observations (expansion, CMB, primordial elements) relatively late, as J.G. points out. 
Cyclic cosmologies have appropriately enough gone in and out of fashion for a long time but generally never been "the" mainstream view. A version is Boltzmann's idea that even a universe in equilibrium will randomly generate localised order from time to time, so there could be new worlds forming just by chance. This is close to the Poincare recurrence issue, where systems constrained to finite phase space volume will eventually have to cycle back to their original state; whether this applies to the universe or not seems to be a bit contentious right now (it depends on whether one thinks the horizon, as per the holographic principle, has a finite entropy capacity, or whether the openness of the expansion makes the phase space expand). 
A: As explained here, until c. 1965 there wasn't even a consensus behind the Big Bang, with many physicists preferring a steady-state model to one in which the universe has expanded for billions of years. Later that decade, Hawking's showed general relativity wouldn't allow for an oscillating-universe model, although a quantum treatment of gravity may be different in this respect.
The expanding-universe consensus initially favoured a decelerating expansion, but the 1980s undermined this description of the Early universe due to the inception of inflationary models. The universe's long-term fate later saw a similar change of view due to the 1990s discovery of contemporary acceleration. This favoured a Big Freeze (formerly called a Heat Death) over a Big Crunch, although a Big Rip still cannot be excluded. I don't know how the relative support for Freeze and Rip have compared since acceleration was confirmed.
