1. Arminians don't believe in the sovereignty of God.
Arminians believe very much in the sovereignty of God.
To say that God gives people freedom does not necessarily mean that God relinquishes his authority over mankind. To be sovereign does not mean that one always has to be in meticulous control over everything that happens. God, for the Arminian, could shape all human events according to his will, he just chooses not to. This is still sovereignty.
2. Arminians believe that Christians could lose their salvation if they commit a really bad sin.
This is not true. Mainstream Arminianism has traditionally taught that the only way one can forfeit their salvation is through a permanent loss of faith. All sins, no matter how bad, are covered by the cross of Christ. Roman Catholicism is the only mainstream tradition that teaches that really bad sins ("mortal sins") can cause one to lose their status in heaven.
3. Arminianism is Pelagianism
This is one of the most widely taught misrepresentations, primarily among Calvinists. Pelagianism is the belief that man is born morally neutral. As well, Pelagianism teaches that man's will is neutral from birth. Therefore, according to Pelagianism, man does not need the grace of God to live according to his will. Arminianism, on the other hand, believes that man is completely dependent upon God's grace in order to be saved.
4. Arminianism is Semi-Pelagianism
Unlike Pelagianism, Semi-Pelagianism is the belief that man is born in a state of moral brokenness but, in his natural state, is still able to call upon God for aid. Arminianism, on the other hand (and like Calvinism), does not believe that man can do any good whatsoever outside of God's intervention. Man, in his natural state, is at enmity with God. It is only the prevenient grace of God that gives man the ability to call on Him for mercy.
Arminians believe in the doctrine of total depravity to the same degree that Calvinists do.
5. Arminians follow a man, Jacob Arminius.
Arminianism represents a system of theology that has roots all the way back to the early church. In fact, it could be easily argued that the earliest Christians after the Apostles were more Arminian than Calvinistic. The designation "Arminianism" is named after Jacob Arminius. Arminius was a Protestant leader who rejected many of the beliefs of the Calvinists of his day, offering an alternative to the prevailing Reformed thought.
6. Arminianism is heresy.
Many passionate Calvinists call Arminianism heresy, but this is normally due to a misunderstanding of both Arminianism and heresy. A "heresy" is a departure from a central belief in historic Christianity. Simply believing something is really wrong does not automatically make it heresy. Most people believe heresy can only apply to issues involving the person and work of Christ. Arminianism is in no way a departure from Christian orthodoxy. It represents beliefs which have always been legitimately debatable in the church.
7. Arminians believe that Christians can be perfect.
Christian perfectionism is a doctrine that is held by Wesleyan-Arminians, not mainstream Arminianism. Most Arminians do not believe that man can be perfect until the resurrection.
8. Arminians deny God's transcendence.
God's transcendence is his timeless, spaceless, matterless existence. Open Theology believes that God is bound in time and, therefore, not transcendent. While Open Theology is an Arminian theology, it is a very radical form. Mainstream Arminians are not Open Theologians and have always believed in God's transcendence.
9. Arminians deny predestination.
All Christians believe in predestination, including Arminians. Predestination cannot be denied, as it is very clearly taught in Scripture. Arminians deny unconditional predestination, believing that predestination is conditioned on the free-will choice of man.
10. Arminians cannot have assurance of their salvation.
The idea here is that Arminians can never know with certainty whether or not they are saved, since it is possible that they may, at some point in the future, lose their faith, and with it their salvation. But Arminians can have at least as much assurance as Calvinists. Calvinists cannot ever know whether or not they are truly elect. So Calvinists and Arminians are in the same boat. Both of them have to rely on the current state of their faith in order to gain assurance.
11. Arminians believe that man's freedom is the controlling force in the universe.
This is a straw man put together by many ill-informed Calvinists who seek to associate Arminianism with a compromise to liberalism. For the Arminian, freedom is not the controlling force of the universe; God's love is. It is God's love that gives man freedom so that he has the ability to choose him.
12. Arminianism is a compromise to Roman Catholicism
Arminians believe in all five solas of Reformed thought, including sola Scriptura (Scripture is the final and only infallible guide for the Christian) and sola fide (justification is by faith alone). Both of these are expressly anathematized by Roman Catholicism. Arminianism is a legitimate option within the Protestant tradition.
Bonus: Arminians are From Armenia
Armenia is a country and has nothing to do with Arminianism.