How I define railroading:
The characters have no impact on the world around them. The DM has a story to tell, and damned if s/he's going to let the PCs get in the way. NPCs react the same way no matter how the PCs act towards them. NPCs are so powerful (one and all) that there are no means of resisting them. It takes five days to travel to the dungeon. "Oh, we'll get everybody horses so we arrive faster and have more time to stave off impending world badness." It still takes five days to get there. We're only supposed to have three days to save the world, so three days we shall have. We get to within a hair's breadth of killing one of the BBEGs early, and the DM out and out says "I don't care, I'm making a plot decision, he gets away."
Personally, I should probably nudge more often. My players gladly pick up hooks...but they tend to shilly shally around a bit. Once they're on the road, they're good. I started the current season of my campaign at the beginning of December. They've just now embarked on the adventure I thought they'd go on two months ago. There's a lot of sitting around, roleplaying minor interactions with NPCs, listening for rumors in the tavern. I do need to find ways to guide them better towards the real excitement.
In the end, though, I rarely to never disallow what they want to do. The world will react and change based on what they do and what time they allow to pass. If they're rude to the NPC, the NPC will not want to help them. If they steal something, the law will be after them. If they act as heroes, they will be hailed as heroes (at least until some shady person with shady motives comes along).