Next, I'm going to assume your dungeon design is usually 'go in, hack things apart/get the dingus, get out'. I'm going to bet that usually it's going into hostile territory and having no qualms about using violence.
So how about this: Capers. "We need you to get in there and steal this thing. But they can't know it's been stolen." This works if over half your party has social or stealth skills; a group of unintellgient brutes only have a hammer and everything looks like a nail.
I remember there is an adventure that came out at the beginning of 3e called "Three Days to Kill". It just consists of hte PCs being hired to break up a business meeting between a cult and a bandit king. They don't have to slaughter everyone, but just make sure the meeting goes south to ruin any alliance. A situation like that works great.
You could even give them a very open-ended task. "Look, we just need you to bring evidence This guy is a criminal/we just need you to bring him into justice." So now, the PCs can go about framing/investigating OR bountying the guy in any way they want - they could set up an ambush. They could storm his place. It's up to how they conduct it.
Another option: Cons. I once ran a campaign where the party were traveling gypsy con artists. You just let the players take control and go! But this really depends on the party.
Defend the Town: The Party is on the Defensive, having to fortify and defend a town from an onslaught of some kind.
Or battling pirates on a large lake/river.
As the above post, using Dungeons for other environments, use the same plots and just apply them elsewhere. I'm SURE you've done the "Bad guys are going to engage in a ritual to do something bad". Well, instead of putting them in a dungeon, they could instead have several sites in a forest, or several tenement rooms inside a district, and the goal is finding/getting rid of the ritual in a certain time limit.
Finally, don't discount the greatness of random encounters on the road. Not just fights/ambushes, but encounters involving travelers or monsters looking to make deals, odd occurances, etc.