"Once in Christ, Never Out": Truth or Heresy?

Once we are in Christ, can we ever lose our salvation? If not, can it be proven through scripture? Can we "of our own will" choose to forsake Christ, and still be saved? If a person goes into eternity in a backslidden state, will they still be saved? Are we still "sealed until the day of redemption" if we choose to leave God after years of faithful service to him? These are some questions that are derived from a controversial and sometimes-touchy doctrine that is phrased, "Once in Christ, Never Out" or sometimes it is referred to as "Once saved, always saved", "Eternal Security", or "Unconditional Eternal Security".