Certainly the Monkey Island games on the Amiga were top notch. Two of the very best adventure games of all time. Absolute classics. I'm suprised that no one has mentioned another Amiga classic adventure game....
Beneath a Steel Sky
What a brilliant game this is. It's very funny and has superb hand drawn graphics by comic artist Dave Gibbons. One of the best adventure games on the Amiga it is!! The CD32 version is quite funny because it has speech. The game is set in Australia but the main character speaks with an American accent! The text is full of English phrases and sayings that are changed to the American sayings in the speech. LOL.
Still a great game though.