Annihilate is a spell that says, in part: "Destroy target nonblack creature". There are many ways to keep Annihilate from working. For example:
A creature that can't be the target of Annihilate (e.g., because it has shroud or protection from black) can't be targeted or destroyed by that spell (C.R. 115.1a, 608.2b, 702.18a, 702.16b). Neither can that spell target black creatures (C.R. 115.1a).
Also, Annihilate can be countered or otherwise removed from the stack to keep it from working (C.R. 701.5a; under C.R. 116.4 and 608.1, for a spell to resolve, all players must pass in a row while it's on top of the stack). Notably, if Annihilate's target is illegal when it would resolve, it fails to resolve (and no card is drawn) (C.R. 608.2b).