So let's look at that. Wikipedia's statement expands on the cited reference by specifying constant consumption, but let's accept that as standard practice in energy reserve estimate statements:
Dr. Anthony Hayward CCMI, chief executive of BP stated in October 2009 that proven natural gas reserves around the world have risen to 1.2 trillion barrels (190 km3) of oil equivalent, enough for 60 years' supply if consumption is non-increasing, and that gas reserves are trending upward.
A quick check turns up a Motley Fool piece stating that global NG consumption is growing at 2.2% annually, or doubling every 32 years. The ten-year average has been 2.7% for a 26 year doubling.
The "gas reserves are trending upward" comment is consistent with the passage immediately preceding in Wikipedia noting that new discovery estimates are hard to establish, so they're often amended upwards. The increasing reserves noted by BP's CEO aren't the result of new finds, but of revised estimates of old finds. And new gas field discoveries peaked in the 1970s, 40 years ago. We're not finding new gas, we're simply recognizing how much was already found.
Fracking also isn't turning up new gas fields, but is allowing known plays to be further extracted. Again, it's digging further into what we'd already known about.
So: given BP's 2013 report of proved reserved of 187 trillion cubic meters, present consumption of 3,314 billion cubic meters, and an annual growth trend of 2.7%, we'll actually exhaust reserves by 2047. With a 2.2% growth trend, we'll last until 2050.
http://en.wikipedia.org/wiki/Peak_gas
The information is outdated from 2009, we have a lot more than that now since fracking just took off in the last few years.