The Mutara Nebula, with its gas density and static discharges, make
shields "useless," and play merry havoc with sensors.
STIII: A magnetic envelope may permit antineutrons while blocking antigravitons. This suggests physics unknown to us in modern age.
STV: Dropping, transporting, and re-raising the shields of the NCC-1701-A Enterprise requires 15.5 seconds. Cutting out the transporter gap reduces this time substantially.
STVI: A ship may be damaged substantially by torpedos in spite of having shields up, as seen by the substantial damage to the still-shielded Enterprise.
STVII: Shields operate on some particular frequency. An adjustable weapon set to the frequency currently in use (e.g., torpedos, disruptors) may penetrate shielding freely.
The hull armor of a Galaxy class may survive fairly well four direct hits from Klingon photon torpedos; however, a direct hit from the phasers/disruptors of a 20 year old (D12) Bird of Prey can breach hull across five decks.
Soran makes use of a 50 gigawatt forcefield to detain Picard on the surface of a planet. This is not, incidentally, a large device.
STIX: In yet another example of small portable shielding, Picard plans for fleeing Ba'ku on foot to deploy force fields inside a system of caves.