The Quadriga has often born the brunt of caricature in Evangelical circles, and many in Reformed churches have only received their understanding through secondary, and often highly polemical, writings. Dispensationalists are particularly eager to jump on the bandwagon here, since a purely "historical-grammatical/literal" hermeneutic is much more suited to supporting the claims of their system (it eliminates typology).
There were abuses of the practice, especially in some of the more speculative writings of the Middle ages, but when certain things are understood, it is a sound and necessary interpretive method, which is in fact practiced my most ministers in their sermon and teaching prep, whether they realize it or not.
The first thing that must be understood is that the four fold sense should not be seen as four separate meanings, but as meaning with three kinds of application. What is known as the
sensus literalis, the first of the fourfold senses, is what we understand by the historical-grammatical "meaning". It must be readily acknowledged that every interpreter of Scripture before the advent of Modernism took the Scriptures as the very Word of God. Even those who engaged in allegorical exegesis began from the baseline of the literal sense, and understood Scripture from the position of inerrancy.
From there the other three, although often posited as three additional meanings, are better understood as three kinds of application that may be drawn from the
sensus literalis. Any time a minster is preaching doctrine from a text, he is preaching the allegorical sense. Any time a minister is preaching eschatological implications, he is preaching the anagogical sense of a text. Any time a minister is preaching on Christian ethics from a passage, he is preaching the tropological sense of a text. These three senses come out all of the time in the application of our preaching, and we could not do without them.
For example, last week I was preaching from Mark 6:1-6a on the rejection of Christ by his people. I was able to discuss the reactions of the people to Christ as he became the fulfillment of the office of the prophet of Israel (from Deut. 18) as having been foreshadowed by the sufferings and rejections of all of the prophets of the theocracy, who were pointing toward the ultimate rejection of the ultimate prophet by God's people as seen in Christ. That was using (in quadrigatic terminology) the allegorical sense, although we would understand it, along with Paul's use of allegory in Galatians 4, as typological. As well, the sermon showed how their recognition of the divinity of Christ was ultimately demolished by their unbelief, as they couldn't get over the stumbling block of his unattractive humanity foretold in Is. 53 (there is a clear shift seen between vv.2-3). That branched into the anagogical/eschatalogical sense as I spoke of the implications of Christ's ascension and fully glorified humanity, and how the Church militant remains as his humble "body" on earth; a weak and pilgrim people who are despised and rejected by the world as was Christ in his humility. From there the tropological/ethical exhortation focused upon a warning to the New Covenant church, that we, unlike the Old Covenant people of God, would not fail to see the power of Christ's Spirit in the working of what is often a weak and easily despised church, but would in faith embrace the Gospel and its often hidden power in the work of the Church. Just as there were those in OC Israel who could not get past the weakness of Christ's humanity in seeing the work of God, so too there are those who despise the weakness of the NC Israel, and who cannot see past her humanity to the divine work that the Spirit does through the Word, sacraments, and prayer. These are applications of the literal sense, and are not separate meanings, but they are important to grasp (unless you have something other than an amil eschatology, in which case you really would not like the applications of this sermon

).
An essay of note on this subject, although written primarily as a refutation of the higher-critical hermeneutic, is David Steinmetz's essay
The Superiority of Pre-Critical Exegesis. Steinmetz is mainline, and I am not recommending all of his thought, but this particular essay is really one that should be read by every preaching minister, in my opinion.
There are also some great insights in Dennis Johnson's work entitled
Him We Proclaim, which has been mentioned here before, and which also incorporates a more robust hermeneutical approach to sermon preparation. He actually connects elements of Enlightenment higher-critical thought with the strict/exclusive historical-grammatical approach taken by many in evangelical and dispensational circles.
As Bengt Hagglund notes in his
History of Christian Theology, while evaluating both the sound and the speculative in Origen's use of the fourfold sense, "these ways of interpreting Scripture have been employed to some extent throughout the Christian tradition". There is good reason to keep this hermeneutic, and I believe that much modern preaching has been impoverished to the extent that it has focused upon the "literal meaning" at the expense of those other areas mentioned, which are vital elements in the understanding of the life of the Church and in gaining a greater understanding of Christ's person and work.