How many men could fit aboard a viking long ship?

It depends on the size of the ship. There were small(er) ships that typically had spots for about 30 to 40 rowers, but there were some very large longships that were built. The Norwegian King Olav Tryggvason's ship the Ormen Lange, was a particularly large specimen, with room for 64 rowers. There was room for passengers and cargo, however, so just because it held x so many rowers doesn't mean that was all the people it held. Ships were built for different specifications and purposes.