The description for beam weapons states that their damage is reduced by one for each shield they pass through, but at least 2 beams, the anti-bio beam and the fire beam, deal no damage and instead hurt crew and start fires respectively. Do shields block these, block part of them, or do they not affect them?
Beams that do no "damage" are blocked completely by any shield.
kotekzot notes that a Zoltan super-shield (the green shield augmentation on certain classes of ship) will take 2 damage towards its 5 damage limit from beam weapons, however.
The easiest way to test this is with the Slug Cruiser - it starts with the anti-bio beam. Just jump until you fight a ship with a shield, and try firing the beam without any other weapons. Visually, the beam is blocked by the shield, and even after firing it 10 times at an enemy ship I wasn't able to kill even one of their crew.