One huge question that needs answering about long-term human space exploration, preferably before people set out on years-long or even life-long missions, is whether plants and mammals - especially humans - can reproduce and grow outside of Earth's comfortable gravitational field.
Did you know that NASA sent three brave squids to the ISS six years ago? I didn't. Read about it here!
As for all the other research topics, there's a whole directory of ideas and projects that NASA has undertaken listed here on NASA's site.
Finally, the research that started me down this rabbit track today is more Mars-related. In an effort to simulate conditions on the Red Planet's surface, experimenters used the ISS's 'Expose' facility to expose strains of tough, cold-loving algae to the vacuum and radiation of space to see how they would cope. Since Mars's atmosphere has only about 1% of the pressure of Earth's sea-level atmosphere, vacuum is getting fairly close to those conditions - perhaps close enough to draw some conclusions about how some genetically-modified organisms would fare if grown on Mars, out under the sky.
The thinking is broader than the implications for the colonisation of Mars. Scientists are also wondering what this algae can teach us about the possibilities of alien life - whether oxygen-breathing, high-pressure atmospheric life might not be the only way life goes.
It bears thinking about. Our Creator is so stunningly creative - perhaps he has sown life elsewhere that's utterly different in structure to what we know, and it would be amazing to discover and study it. Or perhaps he hasn't, and our ongoing failure to find extra-terrestrial life may tell us a tale that many aren't eager to hear.
Here's the research report on 'BioMex' .
And here's a more readable news article on it.