To combine several of the posts above, the inertial dampeners work quite well. If they didn't, the crew would be a one-molecule layer of past on the rear bulkhead any time the ship accelerated, even in sublight.
When they dampeners do (very slightly) fail, the crew does get knocked around a tiny bit. So what? Have we ever seen anyone go to sickbay because of it? No. In fact, it all seems to work much better than a car hitting a wall at 35 mph. Sure, you're strapped in, but your organs will continue on the same vector, making mush inside your chest.
Now, seatbelts are an absolute necessity in automobiles, and I'm not arguing that anyone take them off. But I think we may forgive Starfleet's inertial dampeners for protecting our crews from unimaginable G-forces, while still occasionally dumping them from chairs.