I think there is a difference between stress and depression, when I was stressed running helped. I had a peroid of depression when all I wanted to do was shut myself away from the world. Running didn't help then it was just another stress on my to do list and I had a break. I have just started running again. I don't wear a watch and try not to put any pressure on myself .
I advise women if their pregnancy has no complications to carry on exercising but to listen to their bodies, not to get overheated and to keep hydrated. As joints are more lax to be careful with weights and to avoid contact sports.
I do encourage walking and swimming / aquarobics even if they haven't exercised before.
seren nos, the reason someone might be advised not to swim breast stroke is more to do with symphysis pubis pain. Also not to good for the back especially if technique is poor, but if it doesn't cause problems no reason not to do it. If only it did bring on labour it would save the NHS a fortune on inductions