LucasArts's adventure games in particular were brilliant examples, and I think their defining characteristic is that they never took themselves too seriously. From a guy called Guybrush Threepwood wanting to become a pirate, to time traveling kids trying to stop a mutated tentacle from taking over the world, the settings just kept getting weirder and funnier.
They had their more serious games too, like Loom which is unique in its tone and gameplay mechanics, and The Fate of Atlantis which, as far as Indiana Jones goes, beats the tripe Lucasfilm was trying to push a couple of years ago.