The ultimate example I know is BG2. Once you come to the city there are tons of people who throw their quest at you and each one must be done at once (says the quest giver, you can do it whenever you like). There are some timed quests in BG2 that make sense (jans family, some in the drow city), but most quest have no timer.
It looks like most people have accepted fake urgency to be normal in RPGs. I do not like it. Urgency can be good in an action game, but not so much in an RPG, especially if the RPG is much about exploration.
I have read something (maybe gamasutra, I am not sure) about Portal1. The final battle has a timer. In the beginning it had no timer, people finished it in 3 minutes and it was not very impressive. Then they added a timer of 6 minutes. Suddenly people needed 4 minutes and they were filled with fear and tension. Suddenly it became much more engaging. The writers were also happy because they need only writing for 6 minutes. But Portal is not an RPG, it has a linear environment and it takes place in real time.
Prof. Dr. Dr. Mad S. Tist
World leading expert of artificial stupidity. Because there are too many people who work on artificial intelligence already