"One thing I've always wondered is what would happen when a light saber met an Borg shield?"

This has been discussed on many a Sci-Fi con panel! (Geek hat on)
The Borg shields only seem to be effective against 'phased energy weapons' and not solid tools or fists, like when Worf uses his Meq'leth (Klingon machete) on them in 'Generations'. Based on the movies, the lightsaber beam seems to act like a solid, so it would very likely be effective against the Borg shields.

If I see a Borg, I'll have the replicator whip up a Browning M2, and see how the shields deal with those .50 cal "solid tools"