Arminius didn't teach anything new, but his shoulders were strong enough to carry the cause of the many non-Calvinist Protestants of his day. While his influence on non-Calvinists was the strongest, I did want to point out on this the 400th anniversary of his death, his influence on Calvinism.
As those familiar with Arminius know, his primary issue with Calvinism was supra-lapsarianism - the idea that the decree of unconditional election logically precedes the decree of the fall. In supra-lapsarianism, God uses the fall as a means of coming up with the end. It's like planning a trip. First you set the destination, then you plan the route. In supra-lapsarianism, God first decides who to glorify and who to destroy, then He plans for man to fall so they will need salvation and punishment in Hell.
Arminius' writings against the supra-lapsarians Perkins and Gomorus focused on that issue, as did his commentary on Romans 9 and his declaration of sentiments. Sub-lapsarianism is treated as an after thought and dismissed as inconsistent. Even his dialogue with the sub-lapsarian Junius was spent on demonstrating that supra-lapsarians went 'that far'. If there hadn't been supra-lapsarianism, I doubt there would have been an Arminius.
How did Arminius' efforts against supra-lapsarianism impact Calvinism? The Canons of Dort are sub-lapsarian, not supra-lapsarian. From the Canons of Dort: Before the foundation of the world, by sheer grace, according to the free good pleasure of his will, he chose in Christ to salvation a definite number of particular people out of the entire human race, which had fallen by its own fault from its original innocence into sin and ruin. Those chosen were neither better nor more deserving than the others, but lay with them in the common misery.... those, that is, concerning whom God, on the basis of his entirely free, most just, irreproachable, and unchangeable good pleasure, made the following decision: to leave them in the common misery into which, by their own fault, they have plunged themselves; not to grant them saving faith and the grace of conversion; but finally to condemn and eternally punish them (having been left in their own ways and under his just judgment), not only for their unbelief but also for all their other sins, in order to display his justice. (link)
Arminius pointed out enough problems with supra-lapsarianism and got enough attention on the issue, that the synod moved away from supra-lapsarianism. No doubt, Arminius' role was contributory rather than individually decisive, but then again, Arminius is best seen as the 'point of the spear' in non-Calvinism, rather than a rogue elephant.
Additionally, Dort adopted Arminus' language regarding a serious call. Here's what Arminius said: Whomsoever God calls, he calls them seriously, with a will desirous of their repentance and salvation. (Works of James Arminius) Here's were Dort picked up the same language: Nevertheless, all who are called through the gospel are called seriously. For seriously and most genuinely God makes known in his Word what is pleasing to him: that those who are called should come to him. Seriously he also promises rest for their souls and eternal life to all who come to him and believe. (Dort)
Finally, Arminius and Dort agreed that God is not the author of sin.
Based on Dort's affirming sub-lapsarianism and a 'well meant' offer of the gospel and denying God is the author of sin, the issue with Calvinism today is consistency rather than blasphemy. What a vital contribution to Calvinism! No doubt, I am seeing the thin silver lining on a huge gray cloud, since Dort condemned Arminianism, but it's good to know the bulk of Arminius' work was not lost on Calvinists.