What is Arminianism?

Arminianism is a school of thought based on the teachings of Dutch theologian Jacob Arminius (1560-1609). Basically it says that salvation is dependent on faith in the substitutionary atonement of Christ. Man can only exercise this faith through the grace of God and the work of the Holy Spirit but man is also free to refuse God's grace. In this Arminianism differs from Calvinism. Arminianism also holds that man, once saved, can choose to fall away from Christ, which again sets it apart from Calvinism. (For an in-depth description see Wikipedia.)
Arminianism is not to be confused with Semipelagianism and Pelagianism, although it often is. The latter schools of though elevate man, and are rightly viewed as heresy, whereas Arminianism holds to the doctrine of the absolute depravity of man. For more on this see Setting the Record Straight by Humble Arminian.
Well-known Arminians include Charles and John Wesley, the founders of Methodism.