Re: Can stalactites grow without a stalagmite and vice versa?

Yes.

As ion-rich ground water percolates into a cave, it is exposed to the air 
in the cave and some of the water may evaporate, concentrating the 
solution and causing mineral crystals to precipitate.  This can lead to 
the formation of a variety of shapes, including stalactites and 
stalagmites.  The exact type and shape of formation depends on many 
factors, the most important of which would be groundwater flow rate, 
mineral content of the water, and humidity of the cave air, which affects 
evaporation.

If the flow rate is low and/or the humidity is low, then water dripping 
into a cave from the ceiling may completely evaporate before it has a 
chance to drip onto the floor.  In that case, the minerals will all be 
deposited on the ceiling and only a stalactite will form.  

If the flow rate is high or the humidity is very high, then the water may 
drip off the ceiling before significant evaporation occurs.  In that case, 
any minerals that do crystalize will likely crystalize on the floor, 
forming a stalagmite.  If there is enough evaportation, however, to form 
stalagmites, then there will likely be some evaporation on the ceiling 
side as well.  I would suspect that it is would be very unlikely to see a 
big stalagmite without any trace of stalactite at all, but it is 
theoretically possible.

Newer research suggests a biological origin for some cave mineral 
formations.  That doesn't change the answer fundamentally, but does add a 
layer of complexity.

David Smith, Da Vinci Discovery Center, Bethlehem, PA USA