As with most required doctrines, this one doesn't stand up well to comparison with what scripture actually says. Let's start with the most obvious evidence, two historical accounts in Acts. Acts 8:14-17 relates how Peter and John were sent to Samaria, to a group who had believed in Jesus, who were even "baptized in the name of the Lord Jesus," but who did not receive the Holy Spirit until the prayer of Peter and John. The second account is Acts 19:1-7, in which a group of "disciples" had already received the baptism of John (and given the use of the term "disciples," one would believe already accepted the message of Jesus' lordship), but who had not even heard of the Holy Spirit, which was given to them when Paul laid his hands on them after baptism. The evidence is pretty straightforward: unless we accept a dispensational interpretation nowhere supported in the New Testament, it is possible both to believe in Jesus and to be baptised in his name, and yet not have received the Holy Spirit.
The second part of this doctrine is the implicit notion that whatever receiving the Holy Spirit means, it's a once-and-done event. Here, too, the scriptural evidence would suggest otherwise. There are, of course, numerous accounts in the Old Testament (particularly the books of Samuel and Kings) where the Spirit of God seems to come and go from the same individuals...usually kings or minor prophets. But even in Acts, it is interesting to note that the same people are shown to have been "filled with the Holy Spirit" at least twice: see Acts 2:4 and Acts 4:31. Furthermore, we learn in Acts 6:3-5 that a condition for selecting the men to serve as the first deacons (this is when Stephen was ordained), was that these be men "full of the Spirit." This requirement is nonsensical, unless there is either (1) such a thing as a believer who has not received the Spirit at all, or (2) at least varying degrees of "filledness" with the Holy Spirit.
Perhaps as intriguing as anything, though, is Paul's statement in 1 Cor. 7:40 that, in relation to a command he's just given, "I think I, too, have the Spirit of God." This claim truly makes no sense if every believer is always-and-forever indwelt by the Spirit.
The principal reason I believe this error matters, is that it allows us to cop out of a major self-examination desperately needed by both individual believers and the church as a body. Here's what I mean: throughout the Bible, when the Breath of God moves in and through an individual or a group, something big happens--and by "big" I do not mean people get teary-eyed or feel a major case of the warm fuzzies. Countless times, it results in the individual prophesying (Num. 11:25, 1 Sam. 10:10, 1 Sam. 19:20, Luke 1:67, Acts 19:6). It can result in people speaking in languages other than their own (Acts 2:4, Acts 10:46). It can also result in superhuman strength (Judges 15:14) or even physical transportation (Acts 8:39). The Spirit of God doesn't always make a splash; Isaiah 11:2 refers to the overall anointing of Messiah's life (though when this actually happened (Luke 3:22 and parallels) it was certainly obvious enough.
An interesting aside here--if the conventional notion of the Holy Spirit and Jesus Christ being persons of the Trinity were true, why does scripture report the Holy Spirit coming on Jesus, not only in Luke 3:22, but also his self-proclamation in Luke 4:18-19? How can one "person" of a "godhead" receive another "person?"Anyhow, my point here is, what is the evidence of the Breath of God blowing through our churches today? It is my stubborn belief that, if God's mighty wind were to blow in our midst, we wouldn't have to do mental gymnastics to believe it, we'd have the evidence smacking us in the face! And if, as I regretfully suspect, those who lead the Body of Christ have so thoroughly quenched the spirit that God has taken his action elsewhere, what are we--what are you--what am I--going to do about it?