Traditionally (I hate 99% of traditions, to be honest), there are two viewpoints as far as "Theology" goes. You have "Reformed" doctrine on one side, with the other bearing the moniker of "Armenianism," though Reformed is just a fancy name for Calvinism. Most people view these two theologies as all that exist in Christianity, but to counteract a basic lack of knowledge on this issue, I'm going to give a basic overview of what these doctrines teach and what's wrong with them, as well as what the Bible truly says about this issue.
Hard-core Calvinism or Reformed Theology is summed up in the acronym "TULIP." Also known as "Five point Calvinism," TULIP theology teaches the "Total Depravity" of mankind, "Unconditional Election" of those destined or chosen to be saved, "Limited Atonement" or that Christ's sacrifice was only for the "Elect," "Irresistible Grace" or that the Elect cannot refuse the drawing power of the Spirit, and "Perseverance of the Saints," which means (in its purest form) that those that are saved will retain their salvation through holy living.
While these doctrines seem harmless on the surface, they are dangerous and unbiblical when studied closely. For instance, while "No man can come to me, except the Father which hath sent me draw him," Jesus said that He would draw all men unto Him if He were lifted up. Simply put, Total Depravity is unbiblical, in that God has placed many things in this world to draw the attention of the lost who have never even heard of God or Jesus Christ (Rom. 1:20).
Also, Perseverance of the Saints is not Biblical Eternal Security by any stretch of the imagination; contrariwise, this doctrine teaches that while salvation can be lost, the "Elect" will always regain their salvation and invariably go to Heaven when they die. This is incredibly unbiblical, and though some that hold to Reformed theology no longer believe this, instead adopting true Eternal Security, this is the doctrine that Calvin taught and is held by those that truly agree with fundamental Calvinism.
Armenianism is very similar to Calvinism except that where Calvinists believe certain people are chosen to go to Heaven, Armenianists believe that God's election is conditional upon faith, and while Reformed theology teaches an invariable return to salvation, Armenianism states that salvation is dependent upon continued holy living, and that those that are saved can actually go to hell.
Of course the biggest problem with this view according to the word of God is that the Bible clearly teaches that once someone in the age of Grace (i.e. Church Age) accepts Christ as his saviour, he is permanently and irreversibly saved. Our sanctification is not based upon our continued clean living, but on Jesus Christ's perfect life. We are perfected in the spirit through His blood, and neither obtaining nor retaining salvation has anything to do with our works.
The doctrines of the Bible on salvation are very clear, so it is somewhat perplexing as to how men such as Calvin came up with such ludicrous ideas. The Bible clearly teaches that God created man with a free will and the ability to choose, and that while man almost invariably makes the wrong choice, God always gives him a chance to make that choice. From Adam through Noah, Abraham, Moses, David, and the prophets, each one had a choice to make, whether to obey God or serve their own will. The concept of a free will is unarguable from any standpoint, especially a Biblical one.
Secondly, the idea of Divine Predestination is out of line. Invariably, one will find that a Calvinist must take a verse out of context or apply it incorrectly to make his doctrinal house of cards stand. While Paul declared that we as a church are predestined to be conformed to the image of His Son, speaking to Christians, a Calvinist will say that means that certain individuals were chosen before creation to go to Heaven, when it simply means that when a man gets saved, he is placed on a path to be made perfect like Christ.
The third and final doctrine of Calvinism which I will contrast against the Biblical position is "Perseverance of the Saints." Paul states that we are "sealed unto the day of redemption" by the Holy Spirit, meaning that we have the seal of God on our souls, marking us as His purchased possession. Also, the entire book of Galatians deals with the theme "Kept by Grace," following up on Paul's in-depth salvation discourse to the Romans. He clearly states, "Are ye so foolish? having begun in the Spirit, are ye now made perfect by the flesh?" He spends the rest of the book clearly showing how that once saved by God's grace, through no effort of our own, we are kept saved the same way: by God's grace without our interference in any way.
Simply put, the "traditional" way of looking at theology is deeply flawed. I personally think that there is too much emphasis put on "theology" and not nearly enough placed on actually believing the Bible. When one interprets the Bible through the cloudy, dingy glasses of his own theological viewpoint, he becomes a private interpreter of the Scriptures, which in reality places him in no better standing than an Atheist or the Catholic Whore as far as correct doctrine is concerned.