(Direct link to the demo and adventures section)
The Sword is the #1 most popular and reliably fun introductory Burning Wheel adventure/demo. It is built to showcase the system - fight, duel of wits, simple contests, the whole shebang - in a manageable format. All the characters have strong built-in loyalties and conflicts with one another, the BITs are strong, it's a really solid demo of the system.
The Gift is less a demo than a full-on adventure suited for convention play and is also very good.
I'd start with those two. They are going to appeal to the same sorts of folks who are drawn to Burning Wheel in general - people who like intense, character-driven play with lots of interesting crunch.