For many so-called "evangelicals", primarily of the "Reformed" tradition, throwing around the term Pelagian or Pelagianism is the theological equivalent of the "boogie man" used by some to scare small children. It is, in most Protestant, and certainly Evangelical, circles considered The heresy. A certain website even categorizes other Christian sites as "really bad theology", practically the worst sobriquet being, "pelagianism is alive and well on the Web".
The problem is Pelagius himself did not teach what has come to be called Pelagianism, which was rather outlined by his disciple Coelestius. Furthermore, the subsequent triumph of the Augustinian position over Pelagianism came, not so much through scriptural debate and theological discourse, but (as happened often during the formative period of the Church and, perhaps of more interest to this discussion, later in 16th Century Holland in the dispute between the Remonstrants and Calvinists) by political subterfuge and, at times, outright bribery.
While most intense debates tend to drive the respective opponents to the logical extremes of their positions, Pelagius' initial position may be summed up simply as "what God commands man is able to do". I think most would agree that his basic principle is sound: "God now commands all men everywhere to repent" so all men everywhere have the ability to repent! Pelagius' position was formulated primarily as a response to Augustine, whose doctrine of grace he felt to be a threat to human responsibility as well as freedom. Pelagius was interested in leaving no excuse for those who would impute their sin to a supposed sinful nature. Pelagius asserted that God made man free and that the power not to sin is in the human nature via creation. He held that Adam's sin is not the sin of all humanity and that it would be absurd and unjust to condemn all of mankind for the sin of Adam. While he admitted that the power of Satan and the flesh were intense, his position was that God gives power to overcome them. He also asserted that every man sins for himself out of his own free will and, thus, infants who died before baptism were not lost due to Adam's guilt.
Interestingly enough, his position on grace seems to me to be quite similar to the doctrine of prevenient grace found in Wesley and Arminian theologians. Pelagius held to a concept of original grace or grace of creation which is given to all men (sound familiar?). Admittedly, he did not view it as a special action of God, but rather simply that which is given men as part of their creation. It might be called, though somewhat of an oxymoron, natural grace, but certainly seems similar to Finney's (and others') postulation of natural ability. Pelagius' view on special grace, or what might be termed saving grace, certainly parallels Finney's. This grace consists, not in the granting of the power to do that which one could not do, but in illumination and revelation to woo and encourage men to do that which they will not do.
Finally, Pelagius asserted a grace of pardon or remission of sin which God grants to those who freely repent. Contrary to the charge that Pelagius denied the need for the grace of God, he asserts that without such grace men cannot be forgiven.