According to the German wikipedia: in Europe, 48% of the plastic bottles were recycled back in 2009. According to the Plastic Recycling Report: in North America, 29% of plastic bottles were recycled in 2010.
It will be hard to get numbers for worldwide recycling rates - and to be honest, what is the value of such a number? I've been to Nigeria in 2009 and 98% of the country don't even have some kind of waste-disposal options. It will take a while until recycling will establish in such countries.
As I've mentioned in this answer, recycled plastics mainly go to asia and africa and are used in the production of clothes and carpets. I've not heard about just piling them up overseas as plastic is still a valuable ressource. The main issue is that most of the plastic bottles don't get into the recycle-cycle again but are simply disposed to generic waste or even worse - into the environment.