There are lots of problems flying two-engined planes on one engine. Asymmetric thrust makes flying the plane tricky. Significantly reduced thrust greatly reduces performance. Managing the engines becomes more complex since you might not treat them the same anymore (especially if one is on fire).

In small multi-engine planes where single-engine flight is marginal, the safety advantage is terribly clear. You have a better chance if an engine fails, but you also have a lot more failures.

It's less of a problem in large airliners, where the margins are higher and the training more thorough. The safety advantage is clear enough that all large airliners have at least two engines. Still, there are accidents that stem from a single failed engine on a multi-engine airliner:

http://en.wikipedia.org/wiki/Kegworth_air_disaster

http://en.wikipedia.org/wiki/American_Airlines_Flight_191

http://www.delawareonline.com/article/20060614/NEWS/60614001...

That last one is not technically an airliner, but it's the same basic category, and I think it's a particularly interesting example as they had four engines, but managed to screw things up badly enough after losing just one to crash anyway.