My school encourages each classroom to have a "buddy room" in the building which with to do projects. I've spent the last five or so years working with the same kindergarten class, and as the years have progressed, we've gotten quite strategic at our projects, with the kids (both my 4th graders and her kinders) having a blast as they get to know their buddy!
We try to do something connected to the month, or if that isn't feasible, we make connections to our current unit of study for PYP (Primary Years Programme.) One of my favorite projects that we do is a buddy book, where the 4th graders and kindergarteners look for things that they have in common, and then write (4th graders) and illustrate (kinders) a book together.
This year, in November, instead of doing the usual Thanksgiving project, we added a technology twist! The Kindergarten room has four iPads, my class has four iPads, and we were able to borrow eight additional iPads from other classrooms. The kids had to illustrate something they are thankful for using the special paper from International Dot Day. From there, they got to bring their "dot" to life using Augmented Reality! It was SO cool!