In "Q Who," right after Guinan informs Captain Picard of the strength of the Borg, the captain orders the shields up. Several moments later, a Borg Drone appears in Engineering, having transported over from the Cube.
Do the Borg have the ability to transport through shields? Apparently not, or else they presumably could have simply beamed over Captain Picard in "Best of Both Worlds" instead of appearing themselves on the Enterprise bridge to fetch him. Perhaps there was a fluctuation or some such in the shields in "Q Who?," which the Borg were able to take advantage of.