I usually find a significant amount of modifications is required in an adventure... the flow just seems too "off" to me in many situations, and the situation of the adventure needs adapting to my campaign circumstances at the very least. I am sort of demanding in this way. Though in many cases I could have just plunked certain adventures into my campaign as is, I think it makes my campaign feel like a more consistent whole if I tie it logically to other aspects of the game. For example, the Banewarrens got retroed in as a part of an already existing "vault complex" that existed in my campaign world, and The Ghost Machine (from To Stand on Hallowed Ground was rewritten to weave the prototype ghost machine and the current whereabouts of its makers into my campaign.
Often, I'll use an adventure to fulfill a specific role... eg, to stage a battle with my own NPC, to place a treasure, etc.
If I find it unreasonable to work a given adventure into the game, then I go in and "strip it for parts". NPCs, maps, situations, encounters are all fair game and might get pulled in piecemeal into my own games. Usually, the first thing to go out the window when I get to this stage is the plot.
Sometimes I'll start with the intention of working a given module in, but eventually it works its way out, and all that is left are the vestiges of ideas that were in it. For example, there was an FFG adventure that features "dark ancient gods of the elves" in an elemental themed adventure. Eventually, the elemental dungeon went away in one of my edits of the campaign arc, and the dark gods of the elves got replaced by far realms entities. The adventure just got used as a placeholder to build my thinking around until it developed beyond the basic ideas.