Lost in Time is...
Back in the day when we bought a PS1, Bugs Bunny: Lost In Time was one of the 20 free games we were able to grab. And though most of the other selections we made were pretty bad, the Looney Tunes game was quite the contrary.
Initially, you find Bugs Bunny digging underground and winding up back in time due to a time machine he accidentally sets off. Merlin, a magician if you forgot, tells him to find clocks so he can return to the past, and thus this sets off the bunny wabbit's hilarious time across time and space (or rather, signature characters and bosses in different scenarios).
The time travel thing, despite being cliche, opens up a mound of possibilities for exploration and character exhibition. Personally, I love the Elmer stone age level, especially because of the boss fight. But the others are equally great, and the humor that the game brings to the table is very, very much appreciated. Matching that are the cartoony graphics which sets the mood perfectly as well as the tight controls and great platforming that you can get from a licensed game.