A couple of years ago we started pressing pennies for the boys at the gift shops that had machines whenever we took a trip. I then found some little penny passports on ebay and bought one for each of them. Now whenever we run onto a machine, the boys love to pick their design, insert their penny and money (usually two quarters) and watch their penny get pressed. Then we put them in the passport booklet for safe and easy storage and my boys can look at them whenever they like.
You can find a list of machine locations at pennycollector.com here. So, whenever you are planning a trip, you can look up machine locations and be ready with shiny pennies and enough quarters to press the amount you need.
My boys love their little penny passports and all the memories inside. My 5 year old even decided to take his passport for his only show and tell day at preschool and all the kids thought it was pretty cool.
This has been a great clutter-free souvenir solution for our family.