Calvinists believe that God has chosen, or predestinated, certain people to either go to heaven or to go to hell.  Armenians believe that man has free will to choose to accept God's gift of eternal life, or to reject it.  There are three major viewpoints to this issue:

1. God has chosen specific people to join Him in heaven while others are left to choose or reject Him.

2. God has chosen everyone to go to heaven, but it is left up to people to follow or reject Him. 

3. God has chosen some people to go to heaven, and other people were not chosen, dooming them to an afterlife in hell.

I stick to the second belief because of the Biblical evidence I have found, however, all three beliefs are believed the world over by different denominations for the same reason I have.  To justify my belief, however, let's go to God's Word.

Ephesians 1:5 - "Having predestinated us unto the adoption of children by Jesus Christ to himself, according to the good pleasure of his will."

One can interpret this passage a number of ways, but one of the simplest ways is below:

God has pre-determined that everyone can become a child of God and go to heaven.

God said that anyone can become a follower of Jesus Christ and go to heaven, He doesn't stop anyone from entering if they choose to follow Him, according to the above verse.

To delve deeper into the two factions (Calvinists and Armenians) will require gathering details on their beliefs. 

Calvinists believe God has chosen certain people, the elect, and these are the only ones who will ever make it into heaven. 

Ephesians 2:8 - "For by grace are ye saved through faith; and that not of yourselves: it is the gift of God." (emphasis in bold is mine). 

Armenians, on the other hand, believe that anyone can reject or accept the call of God in their lives. 

John 3:16 - "For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life." (emphasis in bold is mine).

The problem that I have with the Calvinist belief system is that the verb predestinate in the context of the above scripture means "to determine before".  I've heard it said that this means God has a foreknowledge of who will choose him and who won't.  I don't believe this is the right way to interpret the scripture.  I believe it's wrong to say that God has predestined some people to go to heaven, and some to go to hell.

If one says that God has chosen some people to go to heaven and some to go to hell, then you they saying that man has no free will, which is wrong.  God created humans with free will.  Mankind is free to choose to follow God, or to reject Him.  There is no alternative.

If one says that predestinate means God only has a foreknowledge of what will happen, then they are forgetting that God has say in everything that goes on.  He is omnipotent and not separate from the world in any form.  According to the Bible, Hell is the final separation from God, and nothing else is ever stated as such.  Therefore, nothing we know of exists outside of God, and this includes us.  Since that is the case, then predestinate must refer to something more powerful than an inherent knowledge of what will transpire in the future.

Rather than a passive knowledge, predestination can be thought of God's active knowledge of what is going to happen, not a declaration of what is going to happen in each person's life that they cannot change.  God hasn't made it so that everyone will go to heaven no matter what.  Nor has He placed some people into a life that will lead them to hell.  God has an active knowledge of what is going to happen in the future, meaning that He has influenced future events, whose outcomes He already knows, by just being God.

To spell it out, the Greek verb that was used is "προορίζω" (prooridzō) which means to determine before.  So, God already determined (knows through his omniscient nature) that people can and will become His children.  God hasn't chosen some people to go to heaven and others to go to hell.  That goes against everything God has said before.

John 3:16 - "For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life." (emphasis in bold is mine)

I believe that the word "whosoever" refers to all of mankind, not just specific people.  It is possible for anyone who has ever been created and ever will be created to go to heaven after they leave this earth.  Nobody can argue with the simplicity of that verse unless they are unwilling to be open minded about God's Word.  No secondary sources were used in this interpretation, only God's Word.

God knows what is going to happen in everyone's life before their existence was ever even an idea.  God knows what choices we will make, and whether or not we are going to go to heaven.  He doesn't make our decisions for us, though.  God is so merciful that even if He knows someone is going to hell, He still allows them to be created to give them the opportunity to possibly change the outcome of their life.  He created us all with a free will, and if He stopped creating people because He knew they wouldn't go to heaven, then He'd be taking away the very reason He created us.  We were created with free will to choose God or to reject Him.