How reliable are Lycoming and Continental general aviation piston engines?
Short (pilot's) Answer

"Reliable enough for you to fly behind one, flaky enough that you should always expect them to fail at the least convenient moment."

Short (Mechanic's) Answer

"More reliable than the pilot!"



Longer Answer

You can't really know the failure rate, but you can know the accident rate attributable to engine failures.

The NTSB looked at this back in 1972 and Embry-Riddle still has the report available. It's very interesting reading, and goes into great detail on the specific causes of engine failure.
Totaling up everything they classified as "engine failure" gave a failure-related-accident rate of just under 18 per 100,000 hours (i.e. "Assuming proper maintenance you could theoretically fly 5,000 hours in piston GA aircraft before you'd have an engine-failure-related accident.")
There may be a more current NTSB study on this, I honestly didn't look too hard as I expect the numbers to be broadly similar today.

The 24th Nall report shows 61 "powerplant" accidents (all engine types, and including the propeller and associated systems) - the number is not broken down per 100,000 hours but doing a little extrapolation from their other figures it works out to about 0.4 accidents per 100,000 flight hours (or "Assuming proper maintenance you could theoretically fly 200,000 hours in piston GA aircraft before you'd have an engine-failure-related accident.")

The mechanic's answer of "More reliable than the pilot!" comes into play when you look at the pilot-related accident numbers: In the 1972 NTSB report I cited engine failures made up 13% of the total accident figure. In the 24th Nall report all mechanical accidents were 14% of non-commercial fixed-wing accidents (17% of commercial accidents) - that includes a number of other systems (e.g. landing gear) which are unrelated to the engine.