TEDSKI, the Airbus A320 at United is also a non PW powered aircraft. It has IAE engines. But you're right, when they order aircrafts from Boeing, they do specify PW engines.
United currently has over 40 747-400's, they'll definitely be around for at least 10 more years. It is possible that they order a few more of those if they add more transpacific routes from LAX and SFO. The last 100 was retired recently and the last 200 will also be retired soon, late 2001 at the latest.
It is also possible that they order more 777's to replace the last DC-10's and 747-200's. I think that the 777-300 would be the right replacement for the 747-200. United being the airline that launched the 777 10 years ago, I wouldn't be surprised if they go for the 777-300.