The answer to this question in an unequivocal "no". Jesus makes the exclusive claim in the Gospel according to St. John that he is the "Way, the Truth, and the Life."
(14:6) However, while it seems that I have answered the question, the truth is that I slighly evaded it. What every Christian must believe is that no man can come to the Father except through Christ. What the Christian does not have to say is that the religion known as Christianity is necessary for a person to go to Heaven.
Before I proceed further, I am in no way discounting the role of the Church in Christian life. The Church and her sacraments, her reading and preaching of the Word of God are generally necessary for the Christian's nourishment. What I am saying is that I think it is possible that some people discover Christ outside of the boundaries of we think of as the Church. This does not mean that Jesus is the same as Bhudda. It does not mean that Jesus is the same as Krishna, or any other false deity. What it means is that adherents of false religions, while lacking the fulness of the truth (in some cases greatly lacking), can enter the Kingdom of Heaven because they do the will of the Father. (Mt. 7) This also does not mean, we are saved by what we do. It means that Christ's grace can work through even the followers of a false Religion.
Is this a pipe dream? A way of saying everyone's ok, no need to convince others of Christ? It isn't that. We know of one sure way to reach Heaven and that is Christ and the Church he gave us. But in terms of holding out hope for other people, I offer you the story of the Good Samaritan. Lost in the story of what it means to love and what it means to be neighborly, is the fact that the person doing the loving of neighbor in this story is someone that held to a religion Jesus condemned when speaking to the Samaritan woman at the well in John 4. The whole story is predicated on the questions of "how do I inherit eternal life?" Jesus answers with living out the two great commandments. The parable then indicates that a theological heretic, who believed in God, but believed wrong things about him and worshipped incorrectly (wrong mountain-again a reference from John 4), had done what was necessary to inherit eternal life.
Where does that leave us? Again, evangelism of those holding to the mono-theistic religions which are not Christian is absolutely still a good and necessary thing. We have an assurace of salvation only in Christ. But I think we also have reason to believe that those who trust in God (by whatever name they know him) and seek to live in charity with all men (the great commandments) might join we Christians in heaven.
The answer to the question in the title then is this: We go to heaven because of Christ, but some might find Jesus in places most Christians wouldn't think to look.