There are three principal interpretations of this passage among Protestants and Catholics. "All Israel" might refer to:

1. A future large-scale conversion of Jewish people to Christianity
2. All the Jewish people elected by God
3. All the people of God, both Gentiles and Jews

The first of these views is easily the most popular, and is widely held by premillennialists (both dispensational and classic) as well as some postmillennialists and amillenialists. The second and third views are primarily held by amillennialists.

Large-scale conversion of Jewish people

The most commonly held position on this text is that Romans 11:26 is a prophecy of a future large-scale conversion of Jewish people, which is typically associated with the Second Coming of Christ.

This view was popular among the church fathers, as the Catholic Encyclopedia summarizes:

According to the interpretation of the Fathers, the conversion of the Jews towards the end of the world is foretold by St. Paul in the Epistle to the Romans.¹

Pope Gregory I² and Thomas Aquinas³ take this view, and George Leo Haydock⁴ and the Catechism of the Catholic Church⁵ appear to do as well, though their language may admit alternate readings.

Among Protestants, this view is commonly associated with dispensationalism. The Moody Bible Commentary says:

All Israel should probably be understood to refer to the vast majority of the ethnic people of Israel.

Like others, the commentary specifically understands Paul to not be saying "that in the future every Jew will be saved," nor that he means all Jews in history, but rather the "Jewish people at a given point in time." This interpretation is based on the other uses of "all Israel" in the Septuagint, where the phrase does not necessarily mean every single Jewish person.⁶

Besides dispensationalists, however, many other protestants also accept this interpretation, including classic premillennialists like John Piper⁷ and Wayne Grudem,⁸ postmillennialists like Charles Hodge⁹ and Greg Bahnsen,¹⁰ and amillennialists like John Murray.¹¹

In defense of this position, proponents argue that the surrounding context necessitates interpreting "Israel" as the Jewish people. As C. E. B. Cranfield writes,

It is not feasible to understand Ἰσραήλ in v. 26 in a different sense from that which it has in v. 25, especially in view of the sustained contrast between Israel and the Gentiles throughout vv. 11-32. That πᾶς Ἰσραήλ here does not include Gentiles is virtually certain.¹²

Another argument is that only this view can properly be called a "mystery." Bahnsen says that proponents of other interpretations "overlook how irrelevant, obvious, unmysterious and anticlimatic Paul's declaration would be made."¹⁰

All the Jewish elect

The second view holds that "all Israel" refers to the elect of Israel only—that a future mass conversion of Jewish people, though not excluded, is not taught by the text. It is espoused primarily by some in the Reformed tradition, such as Herman Bavinck, Louis Berkhof,¹³ William Hendriksen, and Anthony Hoekema.¹⁴

Proponents of this view argue that the context does not warrant interpreting this passage as prophecy. O. Palmer Robertson emphasizes that 11:1 and 11:5 "orient this first paragraph of Romans 11 to the question of God's dealing with Israel in the present hour." This current time emphasis is maintained, Robertson says, in Paul's reference to his present ministry (13–14) and the repeated use of "now" in verses 30–32.¹⁵ Similarly, Hoekema argues that these later verses could easily be interpreted as pertaining to Christ's first coming, not only to his second coming.

Hoekema, relying on Hendriksen, also argues that using the phrase "all Israel" to describe an end-times conversion:

does not do justice to the word all [...]. Does "all Israel" mean just the last generation of Israelites? This last generation will be just a fragment of the total number of Jews who have lived on this earth. How can such a fragment properly be called "all Israel"?

To Hoekema, the mystery referred to is the "interdependence of the salvation of Gentiles and Jews." This interdependence, and the partial hardening of Israel, Hoekema argues, is something that has been happening in the past and will continue to happen, until the Second Coming of Christ.

All the people of God

The third view holds that "all Israel" refers to spiritual Israel, that is, all the people of God throughout history, both Jews and Gentiles. Like the previous view, it does not necessarily reject the possibility of a future mass conversion of Jews, but does not see this passage as necessarily prophetic in nature.

This view has some early support from at least one church father, Theodoret of Cyrus:

All Israel means all those who believe, whether they are Jews, who have a natural relationship to Israel, or Gentiles, who are related to Israel by faith.¹⁶

Some have also suggested that Augustine shared this view, based on a passage where he uses language from Romans 11 and calls the elect from both Jews and Gentiles "a truer Israel,"¹⁷ but elsewhere he emphasizes a future conversion of Jews.¹⁸ John Calvin, though apparently also seeing a future conversion of Jews, nonetheless argues that Paul's meaning with "all Israel" is "the whole Israel of God," including both Jews and Gentiles, just as it is in Galatians 6:16.¹⁹

Modern defenders of this view include N. T. Wright, who sees Paul switching the meaning of "Israel" midstream as a rhetorical device:

[Paul] has systematically transferred the privileges and attributes of "Israel" to the Messiah and his people. It is therefore greatly preferable to take "all Israel" in v.26 as a typically Pauline polemical redefinition.²⁰

Another proponent, Lee Irons, challenges the prevailing view's argument that "Israel" in verse 26 should be interpreted the same way as "Israel" elsewhere in the chapter (as the Jewish people) by referencing Romans 9:6, "they are not all Israel that are of Israel," as an example of differing meanings in the same sentence. He also contends that an overarching theme in Romans is a challenge to the traditional "Jewish-only" vision of Israel (citing 2:26, 2:12, and 9:24), and sees the "mystery" as being the same as that of Ephesians 3:6:

This mystery is that the Gentiles are fellow heirs, members of the same body, and partakers of the promise in Christ Jesus through the gospel. (ESV)

References:

1. Catholic Encyclopedia, "General Judgment."
2. Gregory, Morals on the Book of Job, I-30. "[The Holy Church,] having taken in the Gentiles to the full, at the end of the world she converts to herself the souls of the Jews likewise."
3. Aquinas, Commentary on Romans. "The blindness of the Jews will last up to the time when the full number of the Gentiles will come to the faith [...] when the full number of the Gentiles has come in, all Israel will be saved, not some, as now, but universally all." (also archived via WebCite)
4. Haydock, Commentary.
5. The Catechism of the Catholic Church, 1.2.2.7, 674 seems to indicate this view as well, though its language may leave open the possibility of the third view: 'The "full inclusion" of the Jews in the Messiah's salvation, in the wake of "the full number of the Gentiles", will enable the People of God to achieve "the measure of the stature of the fullness of Christ."'
6. Moody Bible Commentary on Romans 11:26. Septuagint examples are Nm 16:34; 1 Sm 25:1; 1 Ch 11:10, 15:25, 19:17; 2 Ch 10:3.
7. Piper, "All Israel Will Be Saved", February 29, 2004 sermon. "[T]here will be a great and stupendous national conversion of Israel some day." "I don't know the details, but it seems to me that Paul does mean that in connection with the second coming of Christ there will be a great turning of Israel to Christ." (also archived via WebCite)
8. Grudem, Systematic Theology, 1099. "[Paul] says that sometime in the future a large number [of Jews] would be saved."
9. Hodge, Commentary on Romans, 371–74: "Israel here, from the context, must mean the Jewish people."
10. Bahnsen, "Gospel Prosperity and the Future of Israel," from Calvinism Today – 4, Vol. III, No. 2 (April 1993). 'By this declaration Paul must have meant by “Israel” what he has meant by the term throughout the chapter: namely, ethnic Jews (his brothers “according to the flesh”).' (also archived via WebCite)
11. Murray, The Epistle to the Romans, quoted in Bahnsen, "Gospel Prosperity and the Future of Israel." "[I]t is the salvation of the mass of Israel that the apostle affirms."
12. Cranfield, A Critical and Exegetical Commentary on the Epistle to the Romans, quoted in Irons, "Paul's Theology of Israel's Future," 8.
13. Berkhof, Systematic Theology, 6.3.1.B. "'All Israel' is to be understood as a designation, not of the whole nation, but of the whole number of the elect out of the ancient covenant people."
14. Hoekema, The Bible and the Future, 139–47.
15. Robertson, “Is There a Distinctive Future for Ethnic Israel in Romans 11?,” chapter 16 in Perspectives on Evangelical Theology, quoted in Irons, "Paul's Theology of Israel's Future", 5–7.
16. Theodret, "Interpretation of the Letter to the Romans," quoted in Ancient Christian Commentary, 299.
17. Augustine, quoted in Ancient Christian Commentary, 298.
18. Augustine, City of God 20.29. Hodge cites Augustine in support of this view (Commentary, 374) and so does Meyer (Critical and Exegetical Handbook, II, 234).
19. Calvin, Commentary on Romans. "When the Gentiles shall come in, the Jews also shall return from their defection to the obedience of faith; and thus shall be completed the salvation of the whole Israel of God, which must be gathered from both."
20. Wright, The Climax of the Covenant, 250, quoted in Irons, "Paul's Theology of Israel's Future," 20–21. See "Romans and the Theology of Paul", section VI.
21. Irons, "Paul's Theology of Israel's Future," 8, 15–21.