Rumors

A Key Element of Sandbox Success
"There is a bounty on goblin heads."
The rumor of bounty can be the start of many adventures. Whether it's bandits, goblins or something more threatening, if the players are interested many sessions of play can result from the activities of their characters as they attempt to deal with the bounty situation. The beauty of sandbox play is that the players can shape the campaign through their choices. Perhaps the way they decide to respond to the bounty situation is to try and convince the authorities to not be offering a bounty for killing a sentient creature. Maybe they decide to act as representatives to broker peace between the goblins and said authorities.
"The old silver mine north of town is haunted."
Everyone loves a good mystery. Places of mystery offer atmosphere and wonder, both desirable features in a game. My preferred style of running a campaign fits with the "sandbox" descriptor in that I like to sprinkle a number of rumors about and watch how the players respond to the setting and the rumors. I have semi-fleshed out adventures associated with each rumor before they hear about it, but am also open to modification based on what the players say and how they choose to proceed. Adding new rumors as the characters travel about is a way to keep the campaign fresh and allows me to respond to ideas generated through interacting with my players. Many times the comments of players, their speculations and questions, will initiate some thought on my part which can be developed into a rewarding chapter of the campaign. By listening to my players and imagining what might be true, I have come up with some good ideas. Players like it when their guesses turn out to be true!
"A wolfman is stealing sheep north of town."
Misdirection is a necessary part of rumor use, otherwise they wouldn't be "rumors". I prefer half-truths rather than complete falsehoods. The rumored "wolfman" might turn out to be gnolls who somewhat resemble a wolf walking upright - at least in the dark and from a distance. Any tracks found could be mistaken as made by a wolf on two legs. The reveal when the characters discover the truth behind the rumor can be mildly humorous and still lead to some challenge and reward.
"They are hiring mercenaries down south."
All a sandbox really needs is the beginnings of a map (which can be mostly in the referee's head), a few NPCs, one or two places of mystery (ruins, dungeon, tower, temple, etc.), a half-dozen or more rumors (some connected to the places of mystery, some involving a promised reward), a conflict between factions, and an opening setting such as a village, roadside tavern or a battlefield. Starting the campaign just after a significant battle (or a shipwreck) can be a great alternative to the "you are sitting in a tavern" opening. Are the characters part of the winning side? Are they on the run because their side lost? What lies on the road ahead? So many possibilities hold the promise of adventure!