hi,
just to add my experience to this thread: my placenta was completely covering the cervix (os) at twenty weeks - i was told there was a slight chance it'd move, but not much, because it was fully covering the exit. i wasn't told to avoid sex, lifting, etc etc, however.
i had a very light bleed at 21 weeks (didn't need to go to hospital, they just said keep an eye on it) but no other bleeding.
i was re-scanned at 32 weeks, by which time the placenta had moved, but only a couple of millimetres (it needs to be aboud 4cm away i think). at 36 weeks it had moved a few more millimetres. at 38.2 weeks - bizarrely - it had moved over 4cm from the os.
after spending most of my pregnancy anticipating a c-section, i went on to have a straightforward natural birth.
my advice (provided you've had no major bleeds or other related problems) is to push for a scan as late in the day to check placental position.
even at 38 or 39 weeks, there's still a chance (ime) that the placenta can move out of the way.
good luck - and try not to worry (easier said than done, i know...)
a x