Monstrous Personalities offers examples of non-combat encounters with monsters, creatures, and critters of the Dungeons and Dragons game.
A messenger approaches the player characters. He bears a message asking the characters to meet with a potential employer, and offering them a fairly significant payment just to attend the meeting. If the characters seem suspicious, offer to allow them to arrange the location of the meeting, with the only specification being that it should be somewhere private.
Everything about this meeting is legitimate, the only potential problem is that those requesting the meeting are kobold chief and 3-5 other members of his tribe. This tribe acted as servants to an elderly dragon who recently died of old age, and now they need protection from other tribes in the area, and from other outsiders who might show up seeking the dragon’s treasure.
What happens from here depends on your players. They could simply take their payment for attending the meeting and it would end there. They could do exactly what the kobold fear and decide to go and try to take the dragon’s hoard for themselves. Or they could accept the offer and this could be the start of a single adventure, or even a campaign where the player characters act as guardians to this kobold tribe.
Should they decide to try to get the treasure for themselves, be sure it is not an easy task. If the player characters don’t take the job, it is quite likely the kobolds will find some form of protection for their treasure, whether they hire another group of adventurers, or purchase some sort of guardian creature.
If they take the job, they will be expected to protect the treasure from any number of possible opponents: parties of adventurers, rival kobold tribes, another dragon. And while the kobolds will be somewhat generous due to their sudden wealth, allowing players unfettered access to the magical items in a dragon’s hoard could swiftly imbalance the game. Either have the magic items missing, already taken by adventurers who took the most valuable objects, or place some of the magic items in a secret room well hidden by the piles of treasure.
The limits of where this encounter leads is only limited by where the players want to go with it.