NiCD and NiMH batteries on "Lithium" drill; yes
Lithium batteries on pre-Lithium drill; no, does not fit (on purpose; Lithium batteries need overcurrent protection)
lower voltage batteries on higher voltage drill; yes, but reduced power
higher voltage batteries on lower voltage drill; no, does not fit (on purpose; reason kinda obvious I think [tongue])
I'm not so sure on the newer drills, but I think it used to be so that a 18V drill with 12V battery would be slower and weaker than a 12V drill with 12V battery.
It seems battery prices have come down a bit, but it used to be so that when buying them in a kit with a drill would make the drill very cheap if you compared to separate battery prices.