In astronomy what phenomena have theory predicted before observations? As far as I know, astronomy is generally an observational science.  We see something and then try to explain why it is happening.  The one exception that I know of is black holes: first it was thought of, then it was found.
Einstein's relativity is middle ground to me, he thought of light beams at the speed of light but obviously could observe gravity's effects.
Anyway, I guess my question is, what are the biggest discoveries that were thought of before they were seen in the sky? 
 A: What comes to my mind are black holes. Their existence was postulated by Karl Schwarzschild in 1916, the theory was refined during the 1960s, but as to their existence, we still rely only on indirect evidence. There was a program to find flashes related to the final stages of the evaporation of a black hole started in 2008, but no hard evidence has been gathered so far. The Hawking radiation (if it truly exists) is too weak to be measured from Earth.
A: Dark matter? Much thought about, and still remains to be seen? :)
A: Well, Halley predicted the return of his comet based on Kepler's laws.  
A: To give a much older example: the correct 3d structure of the solar system as predicted by Copernicus theory (Prolemy predicted 2d structure - position of the planets in the sky - only).
A: Hoyle resonant state of carbon - astronomy predicted an physical phenomenon.
A: Off the top of my head, the Cosmic Microwave Background radiation was hypothesized as a consequence of Big Bang Theory before it was observed by accident by Penzias and Wilson.  Also the light element abundances, also a consequence of BBT, was theoretical and is still being refined today through observations that supported the initial theory.
I don't know what your definition of "biggest discoveries" would be, but volcanoes on Io were theoretical before observed by Voyager 2.  The discovery of the most volcanically active body in the solar system seems kinda big to me, but I am a planetary astronomer.
I think you're going to get multiple people posting several different things in response, so one of us responders should try to agglomerate the responses into a single reply.
Edited to add: Since you've accepted my answer over Andrew's I'll just append his to mine so it's more likely that people who just read the accepted ones will see it:  "Neutron stars were predicted in 1934 by Baade and Zwicky, one year after the discovery of the neutron. They were not observationally confirmed until 1965 by Hewish and Okoye. It's hard to beat a prediction that sat around for 30 years before being confirmed."
A: Neutron stars were predicted in 1934 by Baade and Zwicky, one year after the discovery of the neutron. They were not observationally confirmed until 1965 by Hewish and Okoye. It's hard to beat a prediction that sat around for 30 years before being confirmed.
A: In addition to the others, there are other famous theoretical predictions that were then seen in the sky:


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*Neptune!

*Asteroids. (from the failure of Bode's law)

*Lagrange point objects

*Inspiralling neutron star binaries

*Supernova neutrinos(Colgate and White 1966).

*GZK cutoff
The recent cosmology revolution was a combination of theory and experiment. The theory predictions that were borne out include:


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*CMB fluctuation size and spectrum.

*flatness of the large-scale universe.


As a counterpoint, here are some failed predictions in astronomy:


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*excess solar oblateness, Dicke's idea that the sun's oblateness compensates for a scalar component of gravity.

*Steady state theory: the perfect cosmological principle.

*Static universe: this was Einstein's idea for a spherical eternal universe, which doesn't work both theoretically and experimentally.

*Vulcan--- this was predicted in the 19th century to account for the anomalous precession of Mercury's orbit, the actual answer was GR.

A: The deflection of light by the sun was first predicted by Einstein's general relativity, then observed in a solar eclipse.
A: Aristotle (4th century BCE) first hypothesized that the Earth is geographically divided into three types of climatic zones based on their distance from the equator (circles of latitude). In my opinion, it's the basis of one of the greatest science experiments of antiquity that never was. If the ancient Greek astronomers had been modern scientists in their methods, confirmation of the existence of geographical zones would have been the foundational experiment justifying spherical astronomy.
Another basic theoretical prediction that preceded observation is Earth's rotation, which I believe was first firmly predicted by Newton's celestial mechanics, and experimentally observed of course by Foucault's pendulum experiment in 1851.
