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I remember some of their cries, but not all of them. I usually play with my volume toned down a bit because I'm usually doing something else while playing the game,that requires a low noise level.
One time when I was hunting for Ditto in the Trophy Garden while playing Runescape(XD). I was so pissed after the first Ditto commited suicide, so while looking at the computer screen, I guessed which cry is which Pokemon's, until I found a second Ditto and caught it.
Do you realise that if Poliwag was in the game, you might didn't have a Ditto today? Poliwag and Ditto were the first couple I discovered to have exactly the same cry. The second couple was Charizard and Rhyhorn, which I read on bulbapedia.
I can, sort-of. :S Sometimes when I'm playing one of the handhelds and I am looking through the grass, out of boredom I guess which pokemon has appeared just by it's cry. Generally, I'm right. :D