There are lots of engineering challenges associated with long-term space flight. Many of these are driven by the humans on board the vehicles -- specifically the mitigations required to control health risks.
What are the health risks facing humans on long-term space flights?
There are a number of potential health risks humans face in outer space, though probably the two most important are: microgravity and cosmic radiation.
Microgravity: Even if the ultimate destination of a long space flight is somewhere with reasonable gravity (IE: Mars), the humans on board a long-distance space flight would still experience very low gravity for an extended period of time. From experiments conducted on the ISS, and similar orbital stations, we know that microgravity causes humans to experience bone degeneration, muscular atrophy, and suppressed immune response, for starters. Fortunately, we can mitigate the effects of this slightly by having people exercise regularly and wearing heavy clothing, but it still can cause problems.
Cosmic Radiation: Outside of the Earth's magnetic protection, astronauts on a long-distance flight would be exposed to a lot of high-energy cosmic radiation. This can increase the risk of getting cancer, and generally decrease immune function. Fortunately, the levels of this radiation are ordinarily pretty low, so an astronaut could make it from here to about Jupiter with our current technology before they passed NASA's safety standards for radiation. The problem comes when there's an intense burst of radiation all at once from solar flares. A human, exposed unprotected to a solar flare, would get fried pretty fast from it and die from even a small exposure. Fortunately, however, water (it's actually the Hydrogen in the water) is an excellent insulator from cosmic radiation, and most solar flares give at least some advance warning, so astronauts could essentially lock themselves in the food/water storage area for a few days and wait it out.
Neither of these problems are insurmountable, which is why long-distance space flight is even a possibility, but these are certainly two very important issues that must be kept in mind when planning for this type of mission.
