Reuters (via USAToday.com) reports that by the end of 2007 paper airline tickets could "[go the way of] other rapidly disappearing industry services such as in-flight meals and free pillows." In other words, no more paper tickets.
At least, that's how the International Air Transport Association (IATA)—a global trade organization—wants things to play out. The IATA notes that only about four percent of all tickets issued by U.S. airlines are paper tickets, and the goal is to eliminate them altogether.
Apparently a paper ticket costs an airline $10 "to process" while an electronic ticket costs just $1. Assuming those numbers are accurate, I can see the argument. In fact, I can't remember the last time I was issued a paper ticket for a domestic itinerary (they're much more prevalent on international flights).
So what happens if you still want a paper ticket? I doubt paper will disappear entirely, but expect to pay an extra fee for the convenience.
(But don't expect the airlines to pass their paper-cost savings back on to you. That's just crazy talk.)