In Evangelicalism today, Dispensationalism is everywhere and in every denomination. It rejects the classic Covenantal understanding of Scripture. Covenant theology and Dispensationalism have many differences. Theoblogy holds to Covenant theology and hence finds it important to present reasons why we reject Dispensationalism.
Dispensationalism is a nineteenth-century evangelical development based on a biblical hermeneutic that sees a series of chronologically successive "dispensations" or periods in history in which God relates to human beings in different ways under different Biblical covenants. As a system, Dispensationalism is rooted in the writings of John Nelson Darby (1800–1882) and the Brethren Movement. The theology of Dispensationalism consists of a distinctive eschatological "end times" perspective, as all dispensationalists hold to premillennialism and most hold to a pretribulation rapture. Dispensationalists believe that the nation of Israel (not necessarily the same as the state of Israel) is distinct from the Christian Church, and that God has yet to fulfill His promises to national Israel. These promises include the land promises, which in the future result in a millennial kingdom where Christ, upon His return, will rule the world from Jerusalem for a thousand years.
Classical dispensationalists refer to the present day Church as a "parenthesis" or a temporary interlude in the progress of Israel's prophesied history. Progressive Dispensationalism "softens" the Church/Israel distinction by seeing some Old Testament promises as expanded by the New Testament to include the Church. However, progressives never view this expansion as replacing promises to its original audience, Israel.  In Covenant theology however it is to be noted that the church is not a replacement for the nation of Israel but an expansion of it where Gentiles are "grafted into" the existing covenant community. In other areas of theology, dispensationalists hold to a wide range of beliefs within the evangelical and fundamentalist spectrum.
Though many Evangelicals hold to a dispensational understanding of eschatology, most are unaware of what it teaches as a whole. Here is pastor Steve Garrick with a very good presentation on what Dispensationalism is, followed by an examination of the whole system, with reasons to reject it.
 Blaising, Craig A.; Darrell L. Bock (1993), Progressive Dispensationalism, BridgePoint., Pg 10.
 Elwell, Walter A. (1984). Evangelical Dictionary of Theology. Baker Book House, Pg 322.
 Ryrie, Charles Caldwell (1986), Basic Theology, Victor Books, Pg 508-509.
 Harry A. Ironside. "The Great Parenthesis". "It is the author’s fervent conviction that the failure to understand what is revealed in Scripture concerning the Great Parenthesis between Messiah’s rejection, with the consequent setting aside of Israel nationally, and the regathering of God’s earthly people and recognition by the Lord in the last days, is the fundamental cause for many conflicting and unscriptural prophetic teachings. Once this parenthetical period is understood and the present work of God during this age is apprehended, the whole prophetic program unfolds with amazing clearness."
 Mike Stallard. "Progressive Dispensationalism". "some OT promises can be expanded by the NT. However, this expansion is never viewed as replacing or undoing the implications of that OT promise to its original audience, Israel. For example, the Church’s participation in the New Covenant taught in the NT can add the Church to the list of recipients of the New Covenant promises made in the OT. However, such participation does not rule out the future fulfillment of the OT New Covenant promises to Israel at the beginning of the Millennium. Thus, the promise can have a coinciding or overlapping fulfillment through NT expansions of the promise."
 Vern Poythress (1986). "Understanding Dispensationalists". section 12. "Now some Jews have been cut off from their place in the olive tree, so that Gentiles might be grafted in. But Jews in their cutting off remain cultivated olive branches, and they can be grafted in again. This is quite consistent with the fact that there is only one holy (cultivated) olive tree, hence one people of God, and one root."
 Blaising, Craig A.; Darrell L. Bock (1993). Progressive Dispensationalism. BridgePoint., Pg 13.