Let's start with the obvious: Costs aren't the same everywhere.
You may already be aware of this on some level, but until you've traveled extensively, it isn't something you really understand. The cost of living in major cities can vary by as much as 500% or 1000%, depending on how you want to live. I've found that it's almost impossible to reduce your living expenses as much as you can by living overseas.
Leaving the U.S. and choosing to live abroad (assuming you live in the right place) is the single biggest thing you can do to reduce the amount of money you spend. Period. Yes, it requires changes and sacrifices in other areas of your life, but if you're looking for adventure and to radically cut your costs, nothing can beat living overseas.