Most religious groups? I think perhaps very few religious groups do this, and I hold little respect for them. Their leaders seem more egotistical and hungering for press coverage.
The real problem in the world is ego. And every member of every religion has varying degrees of this. Ego clamors for the seats of power, so all great religions have suffered from the egotistical (self-centered) individuals running the show, from time to time.
What most, if not all, religions seem to be after is that of awakening the sleeping spiritual component within us. Salvation is all about awakening, whether it be through Christianity, Buddhism, Taoism or whatever.
If a Homo sapiens body dies, usually the immortal spirit within remains asleep, and continuity of consciousness is broken by that mortal death. Only when the spirit awakens does consciousness continue unabated beyond mortal death. This is the everlasting life of which the Nazarene teacher spoke.
Both Buddhism and Christianity hint at the answer to your last question. With the reawakening accomplished yet by so few, one is saved from eternal suffering in this mortal realm -- saved from eternal, spiritual sleep.