In this piece I use the terms "salvation," "saved," "being saved," etc. in a reductive sense, only referring to ultimately enjoying the beatific vision of God and participating fully in the wedding feast of the Lamb.
To state my position clearly, I am a Roman Catholic who believes what the Church teaches. I believe that Jesus Christ is "the way and the truth and the life" and that nobody goes to the Father except through Him (John 14:6). I also believe salvation comes through Jesus Christ and "There is no salvation through anyone else, nor is there any other name under heaven given to the human race by which we are to be saved" (Acts 4:12). I further believe that God "wills everyone to be saved and to come to knowledge of the truth" (1 Tim 2:4). While I could cite more scriptural evidence, I think these passages show enough to grasp what we might call the dialectical tension at the heart of salvation.
This tension at the heart of what God has revealed about salvation in and through Christ is important because it is what allows us to consider salvation in light of the complexities of human life. Orthodoxy, it seems to me, usually requires Christians to hold two or more seemingly disparate ideas/concepts/notions in tension. So, when it comes to salvation, as with so many articles of Christian faith, the truth lies in media res (i.e., "in the middle of things").
Two things are axiomatic to any Catholic consideration of who will be saved unto life eternal. First, universalism has been condemned by the Catholic Church as a heresy. Second, without Christ and His Church nobody at all would be saved. To keep this simple and in scope, I take the doctrinal formulation extra Ecclesiam nulla salus ("outside the Church there is no salvation") as simply pointing us to the necessity of the Church for salvation. The Church, even for those saved seemingly apart from her, plays a necessary role in the salvation of any and all who are saved. When we consider that the Church is not limited to those alive on earth at any given time but that it also consists of the souls in purgatory and, more relevant to this matter, the saints in heaven who constantly intercede for us, this makes great sense.
I believe people can be saved in an extraordinary manner, that is, without having explicit faith in Jesus Christ or receiving the sacraments. It's important to note that extraordinary means outside the norm. So this belief should not result in being presumptive about knowing who God will save in this way, lest we become damnably lax. The normative way to salvation is by coming to explicit faith in Christ and receiving the sacraments, particularly Baptism. I do not believe for one moment that people who do not have faith in Christ and who do not belong to the Church, even those who have never had the Gospel preached to them in a compelling manner, are automatically saved. To my mind, this is the main reason why the Church, by her very nature, is missionary, tasked by the Lord Himself to "make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the holy Spirit, teaching them to observe all that" Jesus has commanded us (Matt 28:19-20). This is part of what we mean when we confess the Church to be "apostolic."
As a faithful Roman Catholic I believe in heaven, purgatory, and hell. Based on my grasp of the Church's teaching and the testimony of the saints, I don't believe hell is empty. Neither do I presume to know who is in hell or who will be in hell. I believe damnation is eternal and unending. I am content to let God, who alone knows all and who alone is both perfect justice and perfect mercy, judge each person. I think perfect justice and perfect mercy, while distinguishable, are bound so tightly together that you can't have one without the other.
When it comes to what happens to anyone after death I make no presumptions either way. I simply commend the dead to God. The only exception to this rule is those who the Church recognizes as venerable, blessed, or as saints. I have known people about whom I could say, "If s/he isn't in heaven there is much hope for the rest of us" and those who I pray God has mercy on their souls. While I hope I am many years from passing from this life into eternity and that by God's grace I will be saved, I am quite certain I fall into the latter category. Hence, I hope that after my passing there are people who implore God on my behalf.
I also believe purgatory to be populated and so I believe in praying for those in purgatory and seeking indulgences on their behalf to help them on their way.
Among Christians I don't think anyone who has reached the age of reason, especially those who have lived into adulthood, can presume that his/her salvation is guaranteed. I certainly do not believe mine is.