Major airlines really want you to book round-trip tickets with a Saturday night stay to get discount fares. That's because short weekday and one-way trips are dominated by deep-pocketed business travelers.
One way to get around the Saturday night rule is to book on a smaller, budget airline--or even just on a route that a budget airline serves. Budget airlines generally charge by the leg, not by the round-trip, and don't penalize for lacking a Saturday stay. Major airlines then try to compete--once JetBlue came to the New York-New Orleans route, for instance, Delta slashed its one-way fare to half that of a round-trip.
"Throwaway" ticketing, using only the first half of a discount round-trip for a one-way ticket, is a perfectly legal practice frowned upon by the airlines, but they don't pursue offenders particularly zealously.
A risky way to reduce weekday round-trip fares is to book back-to-back tickets. Buy two cheap round-trip tickets on different airlines--one that leaves your point of origination and one that leaves your destination--and use only the first half of each. If you buy both tickets on the same airline, their computer system will probably detect it and you will be found out. And if you do this often, even on different airlines, they'll start inquiring as to why you only fly the first halves of your tickets. Airlines hate it when you do this (even though it's technically legal), and they'll void the tickets and penalize your frequent-flier account if they catch you.