This is one every Christian should feel strongly about. The Bible says that anyone who hasn't accepted Jesus into their hearts will go to Hell, and it's true. We are all sinners and actions, no matter how good, can't atone for what we've done. There are people in remote parts of the world who may never hear the Gospel, but that's what the Great Commission is for: "Go and make disciples of ALL NATIONS." Christians are charged to go out and spread the Word of Jesus to everyone who hasn't heard it and try to make them understand why they need forgiveness.
Evilbible.com says that this means God is judging people on their beliefs rather than their actions. The fact is, if you've truly accepted Christ as your savior that IS an action. Satan BELIEVES in God, but that doesn't mean he's going to heaven does it? Also, if you are truly a Christian that should bring about a radical enough transformation that actions go along with it, without actions you are not a true believer. This doesn't work both ways though, just because you do actions doesn't mean you are a believer.