Imperial Star Destroyers' deflector shields are inadequate in the face of the Rebels' ion cannon, and cannot prevent a small ship from physically latching onto them with a hook; that same small ship presents a real threat to the bridge tower. In general, ramming seems an effective tactic.
Deflector shields are highly effective against turbolaser fire and broadly available, although they have clear limits. Large theater shields are available that can shield against not only incoming fire, but prevent ships from transiting through, although they have limits.
We see very clearly in TESB several tests of an Imperial Star Destroyer's hull strength.
First, the Falcon makes an attack run at the bridge tower. As noted on the STL Travel Page, the Falcon had an incoming velocity of up to 360 m/s while passing by the bridge tower.
We may reasonably estimate that the Falcon has a mass of 400-4000 tons, and (at least initially) impacts on a cross-sectional area of 2-6.3 m2. Empirical armor penetration formulae show penetration depth is related to a term that ranges from V2M/A to VM1/2/A1/4, where V is the velocity, M is the mass, and A the area of impact. As the armoring plates' thickness would seem to be substantially lower than the caliber of the large impacting projectiles, the first formula is strongly suggested.
This suggests comparison of the Falcon with modern day bullets. While we're at it, we also see two key asteroid impacts; one takes out a bridge tower, while another harmlessly glances off the hull or shields of an ISD. Using typical densities and the speeds commonly suggested, we have the following table:
We may note that - incidentally - the 10m rock impacting at around 1 km/s did so from head on towards the highly sloped armor of the ISD. This oblique impact is roughly one quarter as effective at penetrating armor given the angle, placing the actual estimate of penetration (per the USN empirical armor penetration formula) at ~7.7" of face hardened steel. This is sufficient to damage anything short of a battleship, but not an unusual feat of endurance.
Meanwhile, the heavier impacts aimed at the bridge tower (Falcon and large asteroid) would cause devastating and substantial damage to any modern warship, smashing through roughly 12" of steel armor.
Light fighters are unable to penetrate AT-AT armor or shielding with their lasers. The Falcon's deflector shields, doubled aft, survived several hits while being chased by a Star Destroyer.
Shields appear to usually block weapons fire. However, during the Millenium Falcon's attack run on a pursuing Star Destroyer, the Imperials raise shields; the Falcon grapples without difficulty.
This tells us two things about the shields. First, shields are expected to help against a ramming attempt in some fashion. Second, those very same shields are ineffectual against a grappling hook.
This would appear to be a puzzling inconsistency. One possible solution is that the shields have gaps large enough to admit a grappling hook, but not large enough to allow a small freighter to pass. Another is that the the shields would have been ineffectual, but that the Imperials' instinct was to raise them anyway when faced with an immediate threat.
The Rebels' "energy shield" over Hoth is interesting. First, it clearly prevents anything from passing through, and covers a substantial area. Incoming fire, outgoing fire, Rebel ships, and Imperial ships cannot pass through the shield. This suggests that it is a different type of shield than used aboard warships, which have little difficulty in firing while shields are up.
Second, it is somehow possible to get ground troops to the Rebel base without the shield being dropped. It seems most likely that the Hoth shield was not very well fitted to the terrain of Hoth, leaving a substantial gap between the shield's lower edge and the ground.
Falcon flies by bridge at 146 m/s.
Falcon averages 535 m/s while flying at ISD.
discusses armor penetration formulae
ISD bridge smashed by 57m long asteroid.
Asteroid was 70m, bridge tower survived.
ISD survives 10m asteroid with 2 TJ
No, bridge tower really was smashed.