Does anyone know if you can crash into star bases or astoids of other ships?

If you consider bouncing off of them "crashing", sure.

Collisions only do damage to your ship or other ships when you are using the Ramming Speed ability. Also, outside of the Starbase Defense missions, Starbases do not have a health bar and thus can not take damage.

Ok thanks, kinda like in Battlestar Galactica Online.

If we could actually "crash" into things, Admiral Quinn would have stripped me of my science commission long ago for all those dents I put in the hull of ESD with my Recon Science Vessel... one of the consequences of installing powerful impulse engines into the thing...

My officers keep commenting that if they gave their wives keys to their 'Honda' Odyssey they would do nasty things to our 200,000 dilithium starbase windows

I can hear them spouting Jeremy Clarkson like sermons about "turning the collision detection off" from here.

Actually I think collision damage would be an interesting addition and it would add a level of realism missing in the game. STO is one of the few MMOs out where you can actually bump into objects, get jostled by pedestrians in a crowd, etc., but the realism ends when your ship hits an object, bounces off a station, comes to a dead stop after flying head first into a planet.
I'm constantly embarrassed by my Odyssey or rather my driving when it coasts long after I've hit stop (The Odyssey most certainly does not stop on a dime) then crashes into ESD, and nothing looks sillier than that huge ship bouncing off of a planet.
The addition of actual damage when colliding would remind pilots that they aren't flying a bumper car, ramming could be a viable last resort battle tactic, and flying too close to a planet will have very fiery consequences.

i think it would be interesting but with as crowded as they made space i would rather not having it in there. some maps are so full of asteroids that we would be slamming into the all the time during fights