I was a competitive swimmer for 7 years, and people generally swam counter-clockwise, although there have been rare cases where it is the opposite, at my pool which is the same as how we drive in Canada. There is no strict rule here to which side of the lane you swim on.
However, in warm-up at swimming competitions, the lanes would alternate for two more specific reasons than what Will Appleby said. For one, it helps specifically with avoiding the clashing arms in the stroke butterfly. Secondly, it does help a bit with other strokes in that if you are not right beside someone and the lanes stay in sync, there will be no clashing between lanes, but if someone ends up beside you, it is possible more clashing would result.