Many Christians believe that salvation is by predestination, while others believe that salvation is of free will. Predestination means that God, before creation, chose whether each of us goes to heaven or hell. We should not confuse God choosing with whether He simply knows what choice we will all make. Scripture can answer whether salvation is by free will or predestination.
The truth is important here, since if God predestined salvation, the Great Commission becomes pointless (see my page on evangelizing the lost). After all, if God predestined us all, why share our faith at all? What difference would it make?
Salvation: Free Will vs Predestination
God Wishes for Everybody to Go to Heaven
How think ye? if a man have an hundred sheep, and one of them be gone astray, doth he not leave the ninety and nine, and goeth into the mountains, and seeketh that which is gone astray? And if so be that he find it, verily I say unto you, he rejoiceth more of that sheep, than of the ninety and nine which went not astray. Even so it is not the will of your Father which is in heaven, that one of these little ones should perish. (Matthew 18:12-14)
The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance. (2 Peter 3:9)
For this is good and acceptable in the sight of God our Saviour; Who will have all men to be saved, and to come unto the knowledge of the truth. (1 Timothy 2:3-4)
But Not Everybody Will
Clearly, God wishes for everyone to enter heaven (Matthew 18:12-14, 2 Peter 3:9, and 1 Timothy 2:3-4). If God also chose who goes to heaven, as Calvinists believe, we end up with universalism (everybody will go to heaven). However:
Enter ye in at the strait gate : for wide is the gate, and broad is the way, that leadeth to destruction, and many there be which go in thereat : because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it. (Matthew 7:13-14)
Free Will Verses in Scripture
Often, Calvinists will state that the Scripture has no free will verses. Here are a couple free will verses:
Now therefore fear the LORD, and serve him in sincerity and in truth: and put away the gods which your fathers served on the other side of the flood, and in Egypt; and serve ye the LORD. And if it seem evil unto you to serve the LORD, choose you this day whom ye will serve; whether the gods which your fathers served that were on the other side of the flood, or the gods of the Amorites, in whose land ye dwell: but as for me and my house, we will serve the LORD. (Joshua 24:14-15)
I call heaven and earth to record this day against you, that I have set before you life and death, blessing and cursing: therefore choose life, that both thou and thy seed may live: (Deuteronomy 30:19)
God Is Involved in Salvations
Certainly God does play a part in salvations, beyond creating the plan of salvation:
No man can come to me, except the Father which hath sent me draw him : and I will raise him up at the last day. (John 6:44)
Which He will do with everybody:
Jesus answered and said, This voice came not because of me, but for your sakes. Now is the judgment of this world: now shall the prince of this world be cast out. And I, if I be lifted up from the earth, will draw all men unto me. This he said, signifying what death he should die. (John 12:30-33)
However, this drawing is not irresistible:
Ye stiffnecked and uncircumcised in heart and ears, ye do always resist the Holy Ghost : as your fathers did, so do ye. (Acts 7:51)
How Salvations Really Work
The way that I like to describe a salvation is (note that these ratios probably are not exact): A lost person starts 1000 steps from salvation. God takes the first 990 steps; the Christian(s) sharing his (their) faith with the lost person take(s) the next nine; and the lost person takes the final step.
In conclusion, God wishes that everybody will choose heaven, although many will not. He clearly takes part in salvations, to draw people, although people can resist this drawing. Therefore, God gave us free will as far as going to heaven and did not predestine salvation.
 All scripture references are from the King James Version unless otherwise noted. Please see my about page for why I chose this translation.