Just a note to say that I am indeed reading the replies to my original question. It's interesting to see the discussion that has arisen from it; apparently there isn't a real consensus on whether engine failures are universally recoverable or not.
I realize that "always" is a strong word. What I was thinking of was a comparison with fixed-wing aircraft. If you are flying in a fixed-wing aircraft in normal flight (not stalled, and in level flight or a coordinated standard turn, gentle climb or descent, etc.), and the terrain below you is completely flat (think salt flats), it's hard to see how an engine failure could not be recoverable. In every case, you'd be able to glide down to a landing, without hurting yourself or the airplane.
I was wondering if this can also be said of engine failures in a helicopter. You're flying along, or hovering, or are otherwise in some normal regime of flight, and the engine fails completely (or all engines, if you have more than one). Is it always possible to land safely on the salt flat? The original Web page I had read indicated that in certain types of otherwise normal flight, an engine failure means that the aircraft and/or its pilot will be injured or killed. The example given was a failure at 90 feet AGL, which supposedly spells disaster (it was implied that this was from a hovering position at that altitude, rather than forward flight, but I'm not sure).
It sounds like there's a lot of disagreement about whether or not recovery is always possible, and it sounds like it depends a lot on the specific aircraft. I've been looking at YouTube videos of both successful autorotations and unsuccessful ones. The rate of descent is quite harrowing, but apparently that's normal. I think I understand the theory: collective down so that the wind as you descend speeds the rotor up instead of slowing it down, then a flare that reverses the collective so that it briefly produces lift to soften the landing (I hope that's right—probably a vast oversimplification). It looks way, way harder than just gliding onto the ground in an airplane.
In any case, the discussion is interesting.