I generally find that strong, mature Christians do not buy into this as much. However, it needs to be pointed out that this belief is completely false. It does not matter how many good things you do, you are still guilty. I think that part of the reason this is the case is because our culture in inundated with this thinking.
Take a portion from Weird Al's parody "Amish Paradise" for example. Read the lyrics below and you'll see what I mean.
Hitchin' up the buggy, churnin' lots of butterThis song (although a parody) is a secular take at Christian life (albeit Amish) and this portion of quoted lyric is an example of how secular non-Christian people view salvation in Christ.
Raised the barn on Monday, soon I'll raise another
Think you're really righteous? Think you're pure in heart?
Well, I know I'm a million times as humble as thou art
I'm the pious guy the little Amlettes wanna be like
On my knees day and night scorin' points for the afterlife
So don't be vain and don't be whiny
Or else, my brother, I might have to get medieval on your hiney
Paul addresses this clearly for us in Ephesians 2:8-9 where he writes, "For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, lest anyone should boast."
When Paul is speaking of works in verse 9 he is specifically talking about the Jewish customs that one performed in service to God. Paul is writing the church at Ephesus so they know that they haven't been enabled to go to Heaven because they have completed certain religious achievements but because Christ's substitutionary death on the cross atoned for their sins. Just like Christ's death atoned for the sins of the Ephesians, it atones for our sins as well, today.
Christ will judge both the living and the dead (1 Peter 4:5) and the judgment is based on your standing with Him. Are you reconciled to Him or not? Are you forgiven of your sin or not? Are you adopted by the Father or not? Has your sin been removed from your account or not? Is your rap sheet clean or not?
To continue the thought of being judged consider this: You are standing before Christ, the judge, in His court of law. He has all the evidence you could ever want: eyewitness testimony, pictures, video, audio, he knows your thoughts and your heart while you did everything sinful. There is no question, you are guilty of the sin you have committed. You are about to be sentenced, the gavel is about to be slammed down but you object. You say, "Well, what if I can do more good things that will outweigh all of the crimes that I have been charged with?" Do you realize what you are doing? You are bribing the judge with your "good works."
You cannot bribe the judge (especially a judge who is completely good, righteous, just and will not compromise his ways)! If you bribe the judge it usually means you get thrown into prison quicker! This is all assuming that you could somehow outweigh the bad with good deeds.
This is why non-believers are hopelessly lost. If you are reading this and you aren't a Christian and you have thought this way, you need to realize your error. Your crimes aren't going to be erased because you set out to do "good things," not here on Earth and not later when you will be judged for those things.
So how can you stand before a Holy God and have any hope to enter into Heaven? You have to have your rap sheet wiped clean. You need to have your sins pardoned. You need to take your case to the cross.
God says that he "is longsuffering toward us, not willing that any should perish but that all should come to repentance." (2 Peter 3:9) God doesn't want his favorite creation to suffer an eternal death in Hell, separated from Him. He instead wants us to turn away from our sin and turn towards Him. God wants us to stop loving our sin, and start loving Himself. That is what repentance is.
Turn away from what is hindering you from following and loving God supremely and "if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved." (Romans 10:9)
The afterlife isn't based on "points" or a "grade." It is pass or fail.