How much is crystal symmetry dependent on molecule symmetry?
Can one make any kind of inferences on the symmetry of the molecule looking at the symmetry of its crystal or the other way around?
There is only loose connection. If you have molecule that shows C3 symmetry like Ph3P->BCl3 there is a good chance that crystal will have either hexagonal or trigonal cell. On the other side I've seen structure of C2 symmetrical molecule (small metalo-organic) where three molecules built up a helix which led to P3(1) space group.
The only "hard" rule is, as Ivan wrote, is that if your compound is chiral and you are working during crystallization with pure enantiomers (not racemic mixtures) then the space group of crystal must also be chiral. On the other side racemates can give crystals both in chiral (pure or racemic twins) or in centrosymmetric space groups. Eventually you will see quite often, that molecules that in solution have high(er) symmetry are not placed on special but on general position in crystal, what eventually leads to "not quite symmetric" geometry.
To be honest, I don't think you can generally infer any relation between the symmetry of your molecule and the symmetry of the crystal.
Remember that crystallographic symmetry only describe how the asymmetric units populate the unit cell. As such if you work with large chiral molecules (ahem proteins/DNA/RNA) there will be no molecular symmetry.
The asymmetric unit may contain symmetry in the form of non crystallographic symmetry (NCS) which can influence the observed diffraction pattern.
The only general rule as stated by others is that if the molecule that have been crystallized are chiral, then the only allowed spacegroups are the 65 chiral spacegroups. On the other hand if the molecule is not chiral, it could crystallize in any of the 230 possible 3-dimensional spacegroups.