My Background: predominantly Southern Baptist.
Summary: you can have works without faith but not faith without works. Your faith saves you but your works are evidence of your faith. It isn't that your bad works take away your salvation, they just show that it was never there.
Ephesians 2:8-9, along with a number of other verses, clearly state that our faith saves us apart from our works.
"For by grace you have been saved through faith; and that not of
yourselves, it is the gift of God; not as a result of works, so that
no one may boast"
James 2:14-26 explains that our works demonstrate the existence of our faith. Just as Jesus said that a tree is known by its fruit. James also explains that faith isn't just an intellectual assent to facts but it is rather a decision to trust in those facts. He says in verse 19, "You believe that God is one. You do well; the demons also believe, and shudder". Satan believes in God, but he decided not to follow him. A human can believe that God exists but choose not to place his trust in Him.
Christians do sin, but it should be a struggle. Paul depicts this struggle in Romans 7:14:25 where he says, "For what I am doing, I do not understand; for I am not practicing what I would like to do, but I am doing the very thing I hate"(v15). We sin, but we hate it.
1 John 3 talks about this and can initially be confusing. Is says in verse 6, "No one who abides in Him sins; no one who sins has seen Him or knows Him". After reading that chapter one could be left wondering who could ever be a christian. I think the key is verse 9 where it says, "No one who is born of God practices sin", with an emphasis on "practices". This chapter is talking about habitual sin. You will find this explanation in most commentaries that bring up the Greek verb tense means, "does not live a life style of habitual sin".
If you are looking to draw a line with which you can measure if someone is saved or not based on the quantity of sin in their life, then you will probably not find an answer. I used to struggle a lot with that. In the end I realized that I was asking the wrong question. How would an answer help me? Rather than asking, "how close can I get to the line", I realized that I should ask, "how close can I get to God". Then I started living for Him and forgot about the question.
So when you look at a life and you see habitual sin, it should reasonably make you doubt that person's faith and subsequent salvation. There could be people who have good works who don't have faith though. Since I am not God, and therefore do not know the hearts of men, I try not to judge that status of their eternal salvation. However, if their conduct makes me doubt, then I let that drive in me an urgency to make more sure of their salvation.
In conclusion, 2 Peter 1:5-11:
"5 Now for this very reason also, applying all diligence, in your faith
supply moral excellence, and in your moral excellence, knowledge, 6
and in your knowledge, self-control, and in your self-control,
perseverance, and in your perseverance, godliness, 7 and in your
godliness, brotherly kindness, and in your brotherly kindness, love. 8
For if these qualities are yours and are increasing, they render you
neither useless nor unfruitful in the true knowledge of our Lord Jesus
Christ. 9 For he who lacks these qualities is blind or short-sighted,
having forgotten his purification from his former sins. 10 Therefore,
brethren, be all the more diligent to make certain about His calling
and choosing you; for as long as you practice these things, you will
never stumble; 11 for in this way the entrance into the eternal
kingdom of our Lord and Savior Jesus Christ will be abundantly
supplied to you"