What are the chances that you are on plane that has an incident?
I don't know if there is a global compilation. But for Australian operations data exists to allow us to establish a likelihood of being in an incident. Accidents are so rare that it's difficult to get a reliable indicator, however if we are just measuring reported incidents I believe we could get somewhere.  

The Australian Transport Safety Bureau (ATSB) has published an "Aviation Occurrence Statistics" report covering 2004-2013.

Let's focus on high-capacity RPT operations, because lets face it, that is probably what most people are interested in. 

According to the report, in 2013, there were 597,000 departures of Australian-registered high capacity RPT or charter flights (unfortunately the report doesn't seem to split it into RPT only, possibly because we have a lot of high-capacity charter flights to the mines). In the same year there were 3292 reported incidents to the ATSB and 2 accidents. Therefore I would conclude that if in 2013 you boarded an Australian-registered high-capacity RPT or charter flight, your chances of being in a reported incident were around 0.5%, and chances of being are an accident is 0.06%. The incident percentage is approximately the same for the couple of years prior, so I am confident that this remains around about the mark today - though I would not consider the accident rate to be reliable because there were so few.  

The incidents cited in this data vary from loss of separation to a pilot being sick to birdstrikes. 

Have a read of the report but before you take it as gospel, keep in mind, as they say, "there are lies, damn lies, and statistics!"