I'm from Ireland and the answer is no you don't need a passport to travel from GB to Ireland but the airlines will insist on photographic ID so a passport or driving licence is essential. I think the fact that you don't need a passport only applies if you a British citizen though but I'm not 100% on that.
As DOB says, technically you don't need a passport to travel between the UK and the Republic of Ireland. You need a passport if you're travelling from anywhere else though.
The only thing I'll say is that if you're non-caucasian and a UK citizen, you should bring evidence of this (even if you're travelling by ferry) as immigration has got very sticky in Ireland in recent years.
Erm Jenstar, I could go to France from England and I would need my passport then so why should it be different if I flew?
I went to Dublin in January and was told too that I could use my drivers licence, but s*d it, if you've got a passport just use that and take out all of the confusion or fuss.
The same rule applies when travelling to Scotland I believe.