Arminians believe that faith precedes regeneration. According to this doctrine, fallen sinners (due to God's prevenient grace) are able to exercise saving faith (thereby becoming regenerate).
Consistent Arminians also deny the perseverance of the saints. They believe that one who is truly regenerate can lose his salvation.
It seems to me that this makes the doctrine of regeneration superfluous. Regeneration is not necessary in order to be saved. Regeneration does not guarantee that one will stay saved. What good, then, is regeneration? I think this explains why, practically speaking, many Arminians seem to deny the biblical doctrine of the new birth. In its place one often finds a kind of "decisionism" or "decisional regeneration" (i.e. the so-called sinner's prayer).
This is similar to how Arminians treat the doctrine of election. Yes, they believe in (a form of) election on paper. However, when the rubber meets the road, it's a different story. When is the last time you heard an Arminian preach on the doctrine of election (angry, anti-Calvinist rants notwithstanding)?
This is, in my estimation, one of the greatest dangers of Arminianism. In order to preserve this man-made theological system, so many biblical doctrines must be downplayed or redefined to the point where they are practically denied (e.g. substitutionary atonement, total depravity, providence). Ironically, this is the very thing that many Arminians accuse Calvinists of doing.