<font face="Verdana, Arial, Helvetica, sans-serif" size="2">Originally posted by EnhancedByCO:
Simple answer: fly internationally. Most (but not all) international fares permit stopovers of up to 24 hours. Domestic fares usually only permit 4 hour stopovers.</font>
A point of order: connections less than 4 hours on domestic fares, or connections less than 24 hours on international fares, are
not considered stopovers, even if they are overnight. So, if you're on an international flight, you can arrive at, say 4pm, stay the night, and make your next connecting flight at 3:55pm the following day, even if you have a "no stopovers allowed" fare.
It's important to get the terminology right, as you might run into someone that is reading the fare rule that says "no stopovers allowed" and give you grief if you say you want an "overnight stopover." If it's less than 24 hours, it's not a stopover on an international fare as far as the fare rules are concerned - it's just a connection.
As far as I know, this can be done an unlimited number of times along a valid routing. At some airports, you may be subject to a departure tax if you make an overnight connection.