Scumbag
Interestingly enough, easyJet carriers regs say "Passengers must be able to quote their booking reference."
Ryanair now have online check in, so presumably if you turned up and said you had lost your BP, they would be quite happy to trace your reservation and reissue for 40€ or whatever they charge.
I know that secutiy and also immigration occasionally check tickets (it has happended to me a very few times), so personally I always print and carry a copy of the etkt receipt with me.