I seldom use published adventures, but I prefer ones which have a clear beginning and end but more than one way to get between the two. As Frabby says, any linear adventure can deliver a curveball at any time - I was playing in a group doing Temple of Elemental Evil (again) and that particular party got very caught up in the life of Hommlet, the village handily close to the Temple serving as base of operations. We started taking a real interest in the town and its people, arranged for the purchase of some farmland, started up a stud farm (horses had been hard to come by for some reason) and and used local labour to run it.
I've also had several experiences as Vecnath noted - e.g. where having listened to what the players were saying and speculating about the NPCs, I had one town councilman who was until then quite boring and uninspiring, was actually conspiring with a rival NPC adventuring party for riches and rewards and the PCs started to get things happen like while they were fighting the denizens of a kobold fortress, the rival group pulled down the stockade at the back and liberated the prisoners - so when the PCs got back to town, their rivals had taken the credit and received the reward and the party was in full swing... and that was just the start of a great campaign.
Always give the players room to grow - they will usually surprise you when you do.
