Are there any open datasets about manned space missions? I'm looking for basic information like name and nationality of the astronauts or cosmonauts, launcher, goals, time in space, results, and so on.
The Johnson Space Center has a website with biographies of Astronauts and Cosmonauts that you should be able to extract much of your requested information from:
I find it easier to extract from HTML, but the 'time in space' text might be more difficult to extract from the free text than the PDF that Jeanne linked to.
update : oops ... you asked for time in space of the missions, not the astronauts ... Johnson also has a general Manned Space Flight website, which has information about each of the missions (shuttle, ISS, skylab, etc.), but they're each formatted differently enough that it's a bit cumbersome.
If I were you, I'd probably e-mail the contact for those two websites, and ask if they had the information available in more easily parseable form.
There is a current list (April 2013) of astronauts who have flown on NASA missions in PDF format at http://www.nasa.gov/pdf/740566main_current.pdf This contains detailed background information on each astronaut and also includes astronauts from other nations who have flown on NASA missions.
The Apollo By Numbers statistical reference has much of this data for the Apollo missions:
The data is fairly easy to extract and covers astronaut roles, time in space, etc.