In the Star Trek universe, what happens if a ship crashes into another and one has the shields up? What happens if both have shields up?
Obviously, an unprotected ship hitting a shield will be damaged in proportion to the impact momentum. Shields act as physical barriers to matter and high concentrations of energy (you will notice that visible light travels through shields just fine, while high-energy electromagnetic weapons fire is deflected).
I recall either Voyager episodes "Raven" or "Equinox" (or both) containing scenes where shield contact takes place. I recall Seven's shuttle shield-bumping a B'omar vessel, but the Memory Alpha synopsis says phasers were used (my memory may be flawed).
Shield harmonics are important. Shields of differing frequencies will bounce off each other. Impact force will translate to vibrations inside the vessels, which will be handled by inertial dampeners within their limits. Both shields will suffer drains. I cannot recall ever seeing two ships with identical shield harmonics colliding, but I'm fairly certain the shields will pass through each other and the ships will collide hull-on-hull.
Update: As per comment #1 below: When harmonics are matched, instead of a hull-on-hull collision, the hull of the ship with the smaller shield will impact the shield of the other ship.
Update 2: Seven of Nine was once seen walking through a Federation-style containment field (which appear to use the same principles as deflector shields) while her Borg shield was operational. This seems to suggest that a strong field has the potential to overpower the deflective ability of a weaker one.
1: In the remastered version of "The Doomsday Machine", we see the very damaged Starship Constellation take a non-shielded hit from a passing rock, and the hit doesn't inflict further damage to the already damaged starship. (Side Note: To me, that seemed to be a way of saying that even a damaged starship is tougher than an intact star destroyer that does suffer damage from such hits.)
2: Then we see what happens when the ENTERPRISE-E rams the larger Romulan ship, bow to bow, in the Nemesis movie.
3: So will hull integrity affect the outcome of shield-to-shield collisions, or not? From the answers that I've read thus far, all ships seem to be intact during the aforementioned incidents in those examples.