All of the Trivia Quizzes are untimed, unless you select 'Quiz Game' format. There are about 130,000 of these, so that should keep you busy for a while.

Find them, sorted by category, on the left of your screen.
In the various daily/Hourly games, the untimed ones are-
-Brain Teaser
-Quick Question game
-Monster Quiz
-Bus Ride
-Crystal Ball
-Quiz of the Hour.
Good luck!