40GB model was the first one without backward compatibility.

Most units can't, no. However, seeing as something like 2 in 3 households in America have a PS2, I imagine this isn't an issue (I myself have 2 PS2's and a PS3)

Nah you can't. At least not on the slim, my 120 gb PS3's box says its not compatible.

I just keep my old PS2 pluged in next my ps3 It's not too much of an issue/inconvenience for me. But it would have been  nice if all PS3's had been backwards compatable.

Some older models of the 80gig and 40gig PS3 have software emulation and can play most PS2 games. Though there might be slight glitches.

Only if its backwards compatable which is only the first batch (60gb specific I beleive not the lower spec). The current models cant play PS2 games.

Can you play ps2 games on the ps3?