I'm of the opinion that they do exist. As a resident of the Pacific Northwest (I live in Washington), I can tell you that with the amount of dense forest (somewhere in the range of 35-45% of the state), a large intelligent animal could go undetected for a long time without a human coming across it, purely because there is so much area in which to hide. Also, due to the nature of scavengers, a corpse wouldn't last longer than a few days
Not only that, but Native Americans have legends of apelike creatures going back hundreds of years. It could be I believe because I think it would be really cool if Sasquatch is real, but damn it, I believe.