Can I install insulation on the ceiling of an old unfinished basement?
Actually adding insulation is both beneficial for sound reduction and heat retention.  When you insulate your floors you prevent heat loss from your basement, especially if you live in Northern States where it gets cold like me.  This also helps keep rooms at even temperatures which makes your HVAC system operate more efficiently.  Also, if you're outside walls in your basement are not insulated then I wouldn't install it in the floor. As it would be more beneficial to get those outside walls done first then insulate the floor. You'd be well on your way to a finished basement as well.  Python is right about doing it completely or not at all.  Hope this helps!