Mike_flyby,
In 30+ years of flying I have had an engine failure or two, fortunately with no adverse effects other than to the state of my underwear. You mentioned single engine aircraft, and my only experience in this field was in a light piston engine single with an updraught carburettor. Problem was that the bolts holding said carb onto the bottom of the engine came loose. I was lucky in that it happened while on downwind and I managed to complete a forced landing onto the airfield.
In a previous life I used to be in the RAF and in the 20 years that I flew I experienced an engine fire in a Victor, about four engine failures in Shackletons, I had to shut an engine down in a Canberra due to low oil pressure, and the piece de resistance was the night I had a multiple birdstrike in a Canberra, lost one engine immediately and the second one on finals.
If you re-read this letter it almost begs the question "Are multi-engine aircraft safer than singles?" The bottom line, I suggest, is that you frequently practice engine failure drills and, (if you fly singles), keep in practice with PFLs.
However, to put all this into perspective, all thes failures took place over a period of 38 years and nearly 13000 hours, so the statistics are still pretty good.
Don't let the thought of engine failures put you off flying or give you a fear for it. As I was told many years ago - flying is the most fun you can have with your clothes on, so fly safe and enjoy it.