This one’s worth far more than it has any right to be. Memorize these two lists (it should take you about five minutes total) and you’ll never again be puzzled about what prepositions take what cases.

These eight (8) prepositions take the ablative all the time.

a(b)
e(x)
coram
prae
de
cum
pro
sine

These four (4) prepositions take both the ablative and the accusative. When used with the accusative, they imply movement; when used with the ablative, they imply no movement. Hence in + acc. = “into”; in + abl. = “in” or “on”. You’ll notice that the other three of the four are sub/p derivatives.

in
sub
subter
super

There's one other preposition (though it always seems more like an adverb to me -- and the delineation between the two is not as clear as one might think) that takes the ablative or the genitive, and that is

tenus

This is so peculiar, though, that you can go for years without seeing it. I include it more for completeness than because I think you'll find it useful.

All other prepositions take the accusative.