I was always taught to keep the gun pointed downrange and eject the round after 30 seconds.
Over nearly 25 years of shooting, I've had my share of duds, but never an actual hangfire. But then I don't shoot any ammo that's been sitting in a humid South American storage depot for 60 years, either. I suspect hangfires are more common in old-as-dirt milsurp ammo and very, very rare in ammo less than a couple decades old that has been properly stored.
One observation---when shooting pistols and small- or intermediate-caliber rifles either in training or in IPSC/IDPA style shooting, a failure to fire on the range is commonly going to be met with an immediate tap-rack-bang or other failure drill rather than waiting for 30 seconds. But I suppose ejected hangfires aren't as big a deal with small calibers as they are with large calibers or shotgun shells, or in revolvers (a hangfire that occurred after the cylinder had rotated 180 degrees would wreck the gun and probably your hand).