There is NO salvation outside the Catholic Church!

Note:  The following essay should be considered deprecated.  The Catholic Church, plainly, taught for centuries that the sacramental and ecclesiastical unity of the One True Faith was necessary for salvation, but now, with Francis, it is impossible for anyone to be "outside" the Church!  It's just absurd, which means that the Catholic Faith is simply not true, as is the case with all religions.

The first three come from here:

The fourth (and fifth) can be found online.
"There is but one universal Church of the faithful, outside which no one at all is saved." (Pope Innocent III, Fourth Lateran Council, 1215.)
"We declare, say, define, and pronounce that it is absolutely necessary for the salvation of every human creature to be subject to the Roman Pontiff." (Pope Boniface VIII, the Bull Unam Sanctam, 1302.)
"The most Holy Roman Church firmly believes, professes and preaches that none of those existing outside the Catholic Church, not only pagans, but also Jews and heretics and schismatics, can have a share in life eternal; but that they will go into the eternal fire which was prepared for the devil and his angels, unless before death they are joined with Her; and that so important is the unity of this ecclesiastical body that only those remaining within this unity can profit by the sacraments of the Church unto salvation, and they alone can receive an eternal recompense for their fasts, their almsgivings, their other works of Christian piety and the duties of a Christian soldier. No one, let his almsgiving be as great as it may, no one, even if he pour out his blood for the Name of Christ, can be saved, unless he remain within the bosom and the unity of the Catholic Church." (Pope Eugene IV, the Bull Cantate Domino, 1441.)
"Moreover, since subjection to the Roman pontiff is necessary for salvation for all Christ's faithful, as we are taught by the testimony of both sacred scripture and the holy fathers, and as is declared by the constitution of pope Boniface VIII of happy memory, also our predecessor, which begins Unam sanctam, we therefore, with the approval of the present sacred council, for the salvation of the souls of the same faithful, for the supreme authority of the Roman pontiff and of this holy see, and for the unity and power of the church, his spouse, renew and give our approval to that constitution, but without prejudice to the declaration of pope Clement V of holy memory, which begins Meruit." (Pope Leo X, Fifth Lateran Council, 1516)
"For, regulars and seculars, prelates and subjects, exempt and non-exempt, belong to the one universal church, outside of which no one at all is saved, and they all have one Lord and one faith." (Pope Leo X, Fifth Lateran Council, 1516)
Of course, there are many, many more Magisterial quotes, but the above should be sufficient. Any human being who wishes to go to Heaven must end his/her life in "the bosom and unity of the Catholic Church." If there is a "through no fault of their own" category of individuals, however few or many they may be, let the Righteous Judge decide their fate on the Last Day. Until then, we need to proclaim from the housetops:

"Outside the Catholic Church, no salvation."

So, you want to become Catholic, eh?

Well, good for you!  There is nothing like saving one's eternal, immortal soul!!  No matter how miserable you are in this life, Hell will be far more miserable.  Guaranteed.  Getting on the path to eternal life is the easy part.  Staying on that path is more difficult but certainly doable.  It just something which takes work (and works.)  However, with all the heretics running amok in today's Church (there simply isn't enough wood in the World to burn them all), converting to the One True Faith and One True Church can have some obstacles associated with it, all of which, fortunately, are easily overcomed.  So, let's get started:

Architecture says a lot.  If a Catholic parish looks like a Pizza Hut or a water plant, then the folks who attend Mass there (assuming, of course, that such Masses are even valid due to lack of intent on the part of the celebrant) are there to "celebrate life" and not be reminded of the fact that they are miserable sinners who are in need of redemption from the merits of the One and Only Son of God.  Least of all, they do not want to be reminded of the fact that they are destined for eternal and everlasting Hell, especially, from their fornicating and adulterous relationships, etc., etc.

Only heretics abuse the Church's liturgy.  It is heretical, schismatic, false, and scandalous to say that the Novus Ordo liturgy which is celebrated by the Pope (now Pope Francis) is not a valid liturgy, that is, a valid Eucharistic sacrifice.  This means that if the Pope is capable of celebrating a valid Mass and confecting a true Eucharist, other Catholic priests must have the potential of doing so, also.  However, to "play games" with the Church's liturgy is not only disobedient but raises doubts about the intent of the priest celebrating Mass as well as the depositions of those (nearly everyone, in most parishes) who go forward to receive Holy Communion.  So, if you go to Mass and the Creed is never being recited, it's time to go elsewhere!

How often is the Sacrament of Reconciliation celebrated?  If Confession is offered once a month for 15 minutes, what does that say?  (Does anyone ever bother showing-up?)  Yeah, such folks do not believe in Hell (but they will when they get there!)  Don't go to such parishes and do not join the multitude of such "Catholics" who will spend Eternity outside the presence of the eternal One and Triune God.

Does the RCIA program use the new Catechism?  It's not perfect, of course (the Roman Catechism says more using less words), but it's better than most of the catechetical garbage which is out there.  Just ask, indirectly; if it's not "on the list," keep "shopping"!

Silence is golden.  You don't have to tell people why you have decided to become Catholic.  If the catechist asks you (and she will; they are usually women, by the way), just say something to the effect that you "want to learn more about the Catholic faith."  Canon law does not require you to go into detail, and you don't need to argue with anyone about EENS, the Church's moral teachings, etc.

Don't argue with heretics.  If you're sitting in RCIA and the catechist says that the Catholic Church now believes that all infants who die without sacramental Baptism go to Heaven, just curl your lip.  Don't argue with her about it.  You could, if you wish, politely ask her which Magisterial documents teach such a belief, but if you do that, you're just asking for trouble.

Consider a traditional parish.  Christ the King, the Fraternity of Saint Peter, etc., are all parishes who are in full communion with Rome and are likely to be just as orthodox, if not more so, than your typical diocesan parish.  No guarantees, though, and such parishes are not everywhere.  Parishes which have the "Extraordinary form" seem to be more orthodox than those which do not offer the Tridentine Mass.

If necessary, consider the SSPX.  Their sacraments are likely valid, although, they do not like "Feeneyites," but that's a complex topic.  (There are a few written agreements between "them" and "us".)  They are a clique and so you're either going to "fit in" or you're not.  They focus a lot on people's appearance and dress, which means that if you are a woman, you need to show-up in a modest mid-calf skirt with an equally modest and feminine blouse and pretty much commit to dressing that way for the remainder of your life.  Tragically, the SSPX has some racist (and even neo-Nazi) elements to it and can be overly anti-semitic at times, but their theology is very traditional, and if you want a wholly orthodox catechumenate program, the SSPX is hard to beat.  They don't make minorities nor poor people feel welcome, as is evidenced by the fact that there are not many blacks within the Society.  They'll deny this, of course, but it's true.  Do not move across the country to "join" them; it's not worth it!

Avoid the sedes at all costs!.  Groups like the SSPV, CMRI, etc., are anti-Catholic.  Whether they are in a state of material or formal schism is anybody's guess, but they alter the Canon of the Tridentine Mass (omitting the name of the local bishop and Pope) and there is nothing more non-Catholic than that!  Choose the most despicable and heretical parish over them!  Pray instead for the sedes and for their conversion.

Get the diocesan bishop involved, if necessary.  If the local catechist and/or priest is intolerable, then write to the bishop.  It may take him awhile to respond but he will, eventually.  Be specific and tell him that you want to convert to Catholicism.  Again, you don't need to give him any specifics.

It's the Sacraments, stupid!   That's what we're after here.

Remember, anyone whatsoever can administer a valid sacramental Baptism.

If you are a Jew and some heretic priest refuses to baptize you, then have a friend do it.  The CCC describes how:

1284 In case of necessity, any person can baptize provided that he have the intention of doing that which the Church does and provided that he pours water on the candidate's head while saying: "I baptize you in the name of the Father, and of the Son, and of the Holy Spirit."

See my post on baptizing infants for more details.

Could the Catholic Church ever "renounce" her claim on EENS?

Before answering this question ("No!!!!"), consider what the World's leading "village atheist", Professor Richard Dawkins, has to say about the "science" of theology:
But as for theology itself, defined as "the organised body of knowledge dealing with the nature, attributes, and governance of God", a positive case now needs to be made that it has any real content at all, and that it has any place in today's universities.

A dismally unctuous editorial in the British newspaper the Independent recently asked for a reconciliation between science and "theology." It remarked that "People want to know as much as possible about their origins." I certainly hope they do, but what on earth makes one think that theology has anything useful to say on the subject?

What has theology ever said that is of the smallest use to anybody? When has theology ever said anything that is demonstrably true and is not obvious? I have listened to theologians, read them, debated against them. I have never heard any of them ever say anything of the smallest use, anything that was not either platitudinously obvious or downright false. If all the achievements of scientists were wiped out tomorrow, there would be no doctors but witch doctors, no transport faster than horses, no computers, no printed books, no agriculture beyond subsistence peasant farming. If all the achievements of theologians were wiped out tomorrow, would anyone notice the smallest difference? Even the bad achievements of scientists, the bombs, and sonar-guided whaling vessels work! The achievements of theologians don't do anything, don't affect anything, don't mean anything. What makes anyone think that "theology" is a subject at all?
Theology is a dead science, at least for the Catholic modernists, one of whom publicly claimed that the Catholic Church, at the Second Vatican Council, "renounced forever" Her dogma of EENS, that is, the dogma that every human being, without exception and with no exceptions whatsoever (take your pick), needs to end their lives in the "bosom and unity of the Catholic Church."  Of course, we know from the above that such a teaching is de fide, and is the Breath of the omnipotent One and Triune God.  To claim that the One True Church, which is the Catholic Church, has "renounced" the fundamental teaching, "Outside the Church, no salvation", is to claim that the Church has renounced the fact that 2+2=4.  Of course, the true theological sciences, grounded in the One True Faith, teaches us that the Church can never, ever "renounce" the Unrenounceable.  And, of course, the First Vatican Council declared:
Pope Pius IX, Vatican Council, Session 3, Canon 4, ex cathedra: "If anyone says that it is possible that at some time, given the advancement of knowledge, a sense may be assigned to the dogmas propounded by the church which is different from that which the church has understood and understands: let him be anathema."