What was so surprising about accelerating cosmological expansion? The 2011 Nobel Prize in Physics, as far as I understand, concerns the expanding universe -- galaxies moving away from each other at ever increasing speed (that's what I think I read in newspapers). Now, the idea of expanding universe is not new. What is the novelty in this study? What was unexpected in it?
 A: This taken from my Web page at 
http://www.astro.ucla.edu/~wright/cosmo_constant.html
Assuming one virtual particle per Compton wavelength cubed gives a vacuum energy
density scaling like $M_{particle}^4$.
For the highest reasonable elementary particle mass, the Planck mass of 20 $\mu$g, this density is more than $10^{91}$ gm/cc. So there must be a suppression mechanism at work now that reduces the vacuum energy density by at least 120 orders of magnitude.
A Bayesian Argument:
We don't know what this suppression mechanism is, but it seems reasonable that suppression by 122 orders of magnitude, which would make the effect of the vacuum energy density on the Universe negligible, is just as probable as suppression by 120 orders of magnitude. And 124, 126, 128 etc. orders of magnitude should all be just as probable as well, and all give a negligible effect on the Universe. On the other hand suppressions by 118, 116, 114, etc. orders of magnitude are ruled out by the data. Unless there are data to rule out suppression factors of 122, 124, etc. orders of magnitude then the most probable value of the vacuum energy density is zero. 
So the existence of a "small" but noticeable vacuum energy density is very surprising.
A: I'm not sure that the accelerating expansion was so surprising. If the universe is expanding there are only three possibilities, it's expanding at a constant rate, accelerating or decelerating!     
The prize was for the breakthrough observations and careful experimental technique of correcting for the difference in brightness of supernovae to be able to make the measurements.
This discovery didn't answer the more interesting questions of how and why it's accelerating.
A: A decade or two ago, there was uncertainty of the order of 50% about the age of the universe, and its composition. It could have been 8 billion years old, it could have been 20 billion years old. The reason for the uncertainty was that the models of the global universe weren't accurate. This discovery made all the pieces fit together for the first time. It has since been verified by precision CMB measurements, so that the supernovas are definitely good standard candles for determining distances to far away galaxies.
By estimating the velocities of the individual galaxies in large clusters, astronomers could estimate how much dark matter they contain. These types of observations gave the most inclusive estimate for the total matter in the universe, visible ad dark. Relative to the amount required to close the universe, the initial estimate of the density, based on visible matter, was 4% of the critical density. It went up to about 10% when dark-haloes inferred from galactic rotation curves were included, and finally up to about 30% when dark matter in galaxy clusters was included.
But inflationary cosmology predicted 100% with no wiggle room. It was simply inconceivable that the universe could have been so fine-tuned to have 30 percent critical density today , because the fine tuning gets ever finer as you go back in time. So physicists kept pressing the astronomers to come up with the remaining 70%, and they kept on saying they couldn't do it, and this was a source of tension for nearly twenty years.
The measurement of accelerated expansion immediately gave a cosmological constant which would explain the missing 70%, and this gave a correct model, consistent both with itself and with inflation, for the first time. The COBE and WMAP observations (which got the Nobel too) then allowed for the detailed standard cosmological model to emerge.
