Perhaps one of the biggest debates within evangelical Christian circles is the attempt to understand who Christ died for-- more importantly, for whom does His atonement work? This is often referred to as the universality of Christ's atonement, with Arminians generally prescribing to the view that it is unlimited, and that Jesus' sacrifice was made for all and is validated by those who come to accept Him, and with Calvinists, on the other hand, generally arguing that the atonement is limited to those who are of the predestined elect.
Firstly, I do believe that the atonement debate is probably one of the more esoteric disputes that have been espoused since Reformation times. In other words, it's non-essential discourse to which we don't have a commandingly firm answer to, and ultimately a byproduct of a larger debate that questions the role of human responsibility in relation to God's sovereignty. For more on this, I'd recommend John MacArthur's sermon, which exposits wonderfully on the matter. I might feel compelled to write more about it down the road. At any rate, what is essential is that all Christians agree that Christ's atonement is not universal (as in, literally everyone to have lived), but still limited to those who place their faith in Jesus as savior. The question at hand deals with the extent of that limitation.
As someone who prescribes more to reformed theological views, I will not shy away from the opinion that Christ's atonement is indeed limited, in the sense that it is purposed specifically for the elect. Arminians generally counter this view by citing extensively from the Gospel of John, where there are numerous verses that seem to express Christ's salvation as a provision for "all" or "the world" (John 1:29, John 3:16, John 12:32).
The question, of course, is: who is all? As was already mentioned, all certainly does not refer to every human being who has lived, in the sense that all have been saved. However, Arminians would argue that unlimited atonement does authorize Christ's sacrifice for every human being, and that it is up to each individual to choose Christ to complete salvation. Nonetheless, this paradigm still considers "all" as interchangeable with "every human being" and thus still somewhat universalist.
Semantically, however, I do believe that when John refers to "all" or "the world," he is speaking not so much in such universalist tones, but more in the sense of "not just some (i.e., Israel)." In other words, it's important to think about this in the context of the New Covenant, in which Paul declares that "there is neither Jew nor Greek, there is neither slave nor free man, there is neither male nor female; for you are all one in Christ Jesus" (Galatians 3:28). Paul, too, uses the word "all" but is referring specifically to Christians, who are no longer justified by a particular creed or race, as opposed to Jews or Israelites who were formerly bound by the nation-specific Abrahamic and Mosaic covenants in their role as God's chosen people.
Of course, the Church is also "chosen" (1 Peter 2:9) but it's important to note that believers are not chosen by which nation or race they are born into, but rather whether or not they are justified by faith in Christ. In that sense, we can say that Jesus did come to save all.