It all depends upon the seat type, altitude, speed, attitude and orientation of the aircraft during the ejection process. Ejection seats just provide a velocity vector in order to give the pilot enough time to clear the crippled aircraft and deploy the recovery parachute, as this USAF training film shows.
This results in an envelope of airspeed, altitude, and attitude in which the seat can be activated allowing for a safe recovery.
For a so called 'Zero-Zero' ejection seat, it allows for a safe ejection from an aircraft on the ground in level flight attitude. It does NOT guarantee safe ejection from an aircraft in unusual or inverted attitudes at low altitudes or airspeeds.
In the Boeing ACES II ejection seat a basic guide to seat characteristics is given here.
I can't comment on the capabilities of the Russian seats. However the Russians do have a tendancy to be excessivly boastful and colorful with a gullible western press, such as the 1989 crash of a MiG-29 at the Paris Airshow, where the press ran with a story about the K36 seats being able to safely eject at low altitudes and extreme attitudes. The reality was the seat in this incident was activated outside of its safety envelope; the pilot was just lucky he wasn't killed.