At the extremes, there are two different approaches to the "who is saved" question. These approaches intersect in various forms throughout Christian doctrines and the Biblical witnesses (plural - as with most of our big questions, the Bible gives us critical guidance but doesn't give an easy, consistent answer). Different traditions have worked this out in doctrines and practices as varied as double predestination, universalism, forced baptisms or complex tracing of ancestry to save your relatives in past generations. It is a sticky, difficult question.
Here are the two poles, as I see them.
1) Something you do clinches your spot in heaven. At the extreme, this means that you must act in a way consistent with Jesus calling in order to go to heaven. This shows up all over: Be a good person, follow the way of Jesus, get yourself baptized, join a church, take communion, seek out forgiveness and absolution, have faith, serve people, give your money away. Gandhi is often lifted up as a non-Christian who it's hard to imagine in hell because he was such an exemplar of human goodness. There are a variety of actions that fall under this category and there is wide debate about what it is that you have to do to be saved. Residue of this exists in most people's faith consciousness and it can inspire fear for people who ask the question: Am I good enough to be saved?
2) God alone has power over your salvation. The extreme of this approach says it doesn't matter what you do, God will (or won't) save you. Based on this approach, people might argue that Gandhi is in heaven because God's grace would expand to include someone who grew up without the same opportunity to grow in faith as those of us marinated in Christianity. This also covers the vast numbers of people who grew up in the faith but for some reason or another couldn't, with integrity, come to believe. There are an awful lot of people out there who wish they had faith, but just don't and can't force it. The "God's grace is huge" approach doesn't hold those people responsible for not being given the gift of faith.
This is, I think, where people like Rob Bell end up. God is too loving, too gracious, too expansive in mercy to let anyone live eternally separated from God's love. God's power ultimately wins out.
The classic Lutheran (pauline) formulation is saved by grace through faith. This thread is found most clearly in Romans. Grace is the free gift from God, but faith matters because through faith you claim the grace that has already been offered.
Importantly, in Romans, Paul contrasts "faith" with Jewish heritage, not with lack of religiosity altogether. He's arguing that non-Jewish people with faith in Jesus are part of salvation history. As far as I can tell, he isn't exactly addressing the question we are. Someone who is a Biblical scholar, please correct me if I'm wrong on this.
There is always the risk of turning faith into a human work instead of a gift from God and Lutherans work hard to make sure they don't turn faith into a litmus test for salvation. But there is, as one blog comment noted, a wide gray area on this.
Luther is more nuanced on salvation many people give him credit for. Martin Marty interprets Luther in the chapter "Will non-Christians be saved" from book"Lutheran Questions, Lutheran Answers":
God is hidden. Then God is also revealed. Luther says that even when revealed, God remains hidden: who would look for God in the bread and wine of Communion, the water of baptism, smudged ink in a Bible...The startling thing confronts his readers when Luther goes on to say that God is hidden not only in revelation but behind revelation. This is a way of saying that God is God and we are not; the mind of God is other than the human mind; the treasures of wisdom of God are vast, boundless and ours are small and spare and sparse...Our decisions have to be based on the knowledge we have: to share the word of grace, to take the commands of God seriously, to relish and be joyful about the word of salvation that we have received. The rest we leave up to God.The key concept here is humility in the face of God's grace and the mysterious mechanisms of salvation. Opening up the possibility of salvation to non-Christians doesn't need to threaten the faith of Christians who are convinced, because of our encounters with the living God, that Jesus is the saviour of the world. Could it be that God is hidden not only in bread and wine, but also the non-Christian neighbors we've come to love?