The most popular project has been "Squared Rectangles," just like last year, which I adapted from the Exeter problem sets. Here's one sample (they need to figure out five of these, which get progressively harder):
They enjoy these a lot, and there's some nice algebraic thinking that comes into play, but it doesn't seem "projecty" enough... there's not really a conclusion to reach, and I don't know that it really pushes them enough out of the box because there's a set method to working them out. In the future, I might just add these to my "puzzle" center that's available to kids throughout the year and call it a day. But maybe they will wow me with their presentation and convince me of their value.