A few competing ideas exist, and seem to pass in and out of favor depending on the latest science (and often who you ask):
The Big Crunch involves a beginning and an end, but as far as I know makes no predictions about anything else. Bang, expansion, contraction, crunch and done. This model is outlined in Douglas Adams' "Hitchhikers' Guide.." series as I think it was prominent at the time.
The Cyclic Universe is a bang-crunch-bang-crunch universe that is infinite in the time scale, finite in the spacial dimensions. There are no beginnings, but rather expansion and contraction, repeat. It is comforting to think that this is all just cyclical, but we have no way to prove anything "before" or "after," so it's a non-falsifiable claim, much like the Multiverse. If the universe were cyclical or a part of a multiverse or a dream of a unicorn we have no way of testing that, so it's pure speculation unless someone invents a "dreams of unicorns" detector. Maybe they will some day.
The Big Chill scenario involves a definite beginning with an infinite (in time) expansion and cooling leading eventually to everything, including black holes, evaporating away to nothing. Pretty dark and eerie idea, I'm not sure why no one's written a heavy metal album about it yet.
As far as "Crunch or Chill?" that depends on the curvature of the universe and/or the specifics of Dark Energy, both of which are under debate at the moment. More recent data has supported the Chill scenario, but then I've heard some evidence to indicate that Crunch might be making a comeback.
I like Crunch better, but that's a philosophical preference. Seems less like everything is pointless. Or maybe I should just accept it and become a Buddhist?
I am not aware of anyone who supports a "no beginning" scenario. No scientists anyway.