I did a bit of further research on this topic to double check my recollection.
The closed universe theory has been all but disproved. It is no longer given serious consideration. This is in large part due to the fact that the universe continues to expand, and the expansion is accelerating. There is simply not enough mass in the universe to halt the expansion. (This includes light and dark matter, the weight of all neutrinos, etc. The universe has only about 1/5 to 1/10 of the matter needed to halt the expansion.) Hawking (originally a proponent of the closed universe theory) didn't believe this at first, and said, "I thought for many years that the astronomers had simply overlooked something, that there was enough matter to close the universe." He concedes he was mistaken. This is very nicely illustrated in "A Brief History of Time." It's a stellar book (bad pun) but if you can get past the dense and difficult language, the ideas are beautiful.
In January 1998, at the conclusion of the annual meeting of the American Astronomical Association, it was announced that 5 independent studies, each approaching the issue from a different angle, had all come to the conclusion that the universe is almost without question "open", or as one follow-up report put it "destined to expand forever." (See Astronomy Magazine News reports of Feb. 17, 1998: see also the feature article "The Future of the Universe" in the August 1998 issue of Sky & Telescope magazine, pages 32-39 by Fred Adams [U. of Michigan] and Gregory Laughlin [U. of California, Berkeley]).
Before all this data was available, in 1917, Einstein was a big proponent of the closed universe theory. In later years he changed his mind. Then he flipped back again. Then he basically said, "I don't know." Part of his discomfort with the open universe idea came from the fact that his general theory of relativity required a closed universe. That was one reason for his frustration with quantum mechanics, for which his theories didn't work. (Superstring theory attempts to breach the gulf b/w general relativity and quantum mechanics.)
Stephen Hawking, Neil Turok, and even Andrei Linde, (a physicist who disagrees on Hawking's "inflationary" component of the Big Bang, but not the conclusion of the open universe), note that the Big Bang theory is basically proven. (It can't be completely proven, b/c it cannot be falsified.) Three separate facts led to this conclusion, including 1.) The presence in the universe of the precise amount of background radiation predicted by the theory; 2.) The presence of hydrogen, helium, (as well as deuterium and lithium) as the most common elements and of course, 3.) The ever-expanding (and accelerating) universe. (One recent study suggested that the acceleration will pick up in speed in the near future (near that is, on a cosmic time scale)
To sum up, despite having tasted of desire, the universe will end not in fire but in ice (or rather heat death), maximum entropy, and death of all the stars and of course oblivion. So long and thanks for all the fish.
<img src="http://members.aol.com/rnfpantera/hking1">