Below are some prevention ideas, later I'll talk about how to unstick buckets once they are stuck.
1. Toss a stick in each bucket before you stack it.
CONS: Makes the stack of buckets 50% taller. Storage can become an issue.
2. Thread some rope in between each bucket.
CONS: Kind of time consuming to do each day and you have to find some rope.
3. Drill some holes to vent the buckets.
CONS: Doesn't always work and you need a drill.
You can also prevent stuck buckets by reducing the number of buckets that are stacked at any given time. Maybe two or three shorter stacks are safer than one large one.
Avoid stacking buckets from different manufacturers (ex. Home Depot and Lowe's, see photo #2 above). While most buckets are made by just a few companies, buckets of slightly different sizes/shapes are more prone to getting stuck.
Sometimes you'll find a 'problem bucket' that habitually gets stuck. Mark it with some duct tape (maybe a red S? just an idea) or maybe use it for storing sticks or shakers.