I was gonna suggest MI2 but you made a rule against that
..
Well I was also gonna Suggest DOTT cause a feel like replaying that now
Or Sam and Max since well soon be getting a new one
I would normaly agree With Fov's idea of Shadow, but i just finished that with all the endings about a month ago...although its a good game that i wouldnt mind playing through again.
But its not the easyest to get your hands on, it can only be bough second hand and the prices vary quite a bit.