Another weird example is the border between Washington and Oregon. Washington has sales tax, but no income tax; Oregon has income tax, but no sales tax. So if you live and work in Vancouver, WA, but shop across the river in Portland, OR (it's literally just the river separating these two), you can dodge either tax.

(Technically, if you go shopping to Portland from Vancouver, you're supposed to pay a use tax on those goods. But there's no practical way to enforce it, and few people are even aware of it.)