In February 2008, Obama was expressing doubt about the Bush plan for manned spaceflight that would replace the Space Shuttle, the Constellation/Ares/Orion program, and suggested delaying it in order to pay for increased funding for science and education. Some months after that, competing with Hillary Clinton and then John McCain for Florida voters, he reversed and supported the Bush plan, with all the money it entailed in Florida expenditures (and Alabama and Texas, but they weren't in play).
Now Obama has re-reversed and even gone beyond where he was before, cancelling the over-budget and delayed Constellation program entirely. He didn't kill the manned space program (although that would've been fine with me), but instead will contract out the "space taxi" business to get astronauts to the space station, extend the station's life from 2016 to 2020, and redirect money to research on more advanced heavy lift vehicles that could ultimately get humans out of low-Earth orbit, although not in this decade.
To get the best details currently available, read the pdf (especially page 4). None of this is guaranteed, by the way, because existing programs will use their pet congressional reps to fight back. Killing Constellation is good. Extending the space station lifespan is bad but probably necessary politically and diplomatically. The slight increase in space station budget to do some actual science is good but only if we're keeping the station. Switching parts of the manned program to advanced research creates some real-world utility. There's also $3b of that funding for robotic exploration as precursors of manned flight, which could be a good way to sneak actual science into otherwise wasted money.
Science does well, with earth climate observation getting funding it needs, as does research on green aviation. Rightwingers who deny climate change are attacking the funding for climate science, without noticing the contradiction in their attempt to shut down science that they claim will ultimately vindicate them.
They say they're fully funding the Hubble replacement, Juno robotic mission to Jupiter, and already-planned future missions to Mars and Europa. Nothing too surprising - robotic scientific missions have done well (at least in comparison to the manned program).
Then there's my hobbyhorse, the Terrestrial Planet Finder space telescope whose budget was zeroed out by the Bushies in order to fund the manned space program. Because this mission could detect atmospheric spectra on habitable planets on other starts that could provide pretty-conclusive evidence of life elsewhere. So just a potential, partial answer to life, the universe, and everything.
Unfortunately, no answer as to whether TPF is coming back. Page 16 of that pdf I linked to says a new decadal survey will determine astrophysics priorities, which will apparently be released in mid-2010.
We'll see what happens. Meanwhile, I plan to revolutionize everything with a Facebook group I just established called "Launch the Terrestrial Planet Finder Space Telescope!" I'm sure this will make it a lock in the future budget.