As a Boeing Flight Controls engineer who worked on the 777 program from program inception through certification of the 777-200 and -300, let me add my comments to this thread (all comments also apply to the 767, except where noted):

1. Re thrust capability:
Not only can the 777 land with just one engine, it is fully capable of taking off with only one engine operating, even fully loaded with fuel, passengers, and cargo. Should an engine fail during the take-off roll prior to reaching "take-off committal speed", the pilots would abort the take-off. should the failure occur beyond this speed, the aircraft is fully certified and tested to take-off with just the one engine.

2. Re "dead-stick landing":
In the extremely unlikely situation where both engines fail:
- the Auxiliary Power Unit (APU -- a small jet turbine driving a hydraulic pump and electrical generator in the tail) would provide adequate hydraulic pressure and electrical power to the flight control surfaces for landing
- should the APU fail as well as both engines (perhaps due to zero fuel availability), then the Ram Air Turbine (RAT) would deploy, and it would provide sufficient hydraulics and electricity to complete the landing. (The RAT is a propeller-driven hydraulic pump and electrical generator mounted inside the belly of the plane; if needed, the RAT automatically drops down into the air stream, and the airflow rotation of the propeller blades provides the needed drive force).

3. Re the "yaw" response:
On a twin-engine aircraft (eg, 777 or 767), with two normally operating engines, thrust is equally balanced or "symmetric" on the two sides of the aircraft. With one engine failed, the functioning engine must provide much greater than normal thrust on that side, with, of course, zero thrust on the other side; this "asymmetric" thrust condition produces a yawing moment, which can be corrected using the rudder flight control surface. The Fly By Wire (FBW) software of the 777 is programmed to detect asymmetric thrust (ie, an engine failure) and very quickly provide the needed commands to the rudder to compensate -- far faster than any pilot could respond. This quick response is important should an engine failure occur during a very safety critical flight phase (eg, take-off or landing) where the aircraft is in close proximity to the ground.

Note the above comment on FBW software compensation for asymmetric thrust applies only to the 777, as the 767 does not utilize FBW.

4. Re aircraft "dropping like a stone" with loss of both engines:
You may recall the "Gimli Glider" incident -- soon after the 767's introduction into commercial service, on 7/23/83, a 767 operated by Air Canada ran out of fuel midway through a transcon flight (this was due to the incorrect fuel quantity being loaded onboard -- confusion over metric vs English measurement units). Despite loss of both engines and the APU (due to zero fuel), but utilizing the RAT for hydraulics and electrical power, the flight crew operated the 767 as a glider for some distance before very successfully landing it at a deactivated Royal Canadian Air Force field at Gimli, Manitoba. The glide ratio was calculated to be 11:1 - quite high for an aircraft never intended to be a glider.