You can’t find one final judgment scene in the Bible that is not a judgment by works. Salvation, we are told often, is not by works, but final judgment sure is. Here are Paul’s words, and we could back them up with others from Paul and yet others from Jesus (try Matthew 16:27 or 25:31-46):

Romans 2:6: For he will repay according to each one’s deeds: 7 to those who by patiently doing good seek for glory and honor and immortality, he will give eternal life; 8 while for those who are self-seeking and who obey not the truth but wickedness, there will be wrath and fury. 9 There will be anguish and distress for everyone who does evil, the Jew first and also the Greek, 10 but glory and honor and peace for everyone who does good, the Jew first and also the Greek. 11 For God shows no partiality.

Paul’s perhaps quoting from Psalm 62:12 and Proverbs 24:12, but it could just as easily be his own version of something he knows Jesus said.
Here is the logic of Paul’s words:
1. Those who do seek glory, honor and immortality — eternal life.
2. Those who are self-seeking and reject the truth — wrath and anger.
Let’s tie this together with what we have seen earlier in Romans. Seeking glory, etc., has to do with not suppressing truth, not creating idols, but instead seeing through nature into the invisible attributes of God, and observing that Jesus Christ is God’s revelation of the gospel, and that the gospel can save. Self-seekers are those who stop the natural revelation in its tracks and worship this world, who suppress the truth and turn to idols, who turn in on themselves to satisfy their own indulgent natures. For such, Paul warns, there is wrath and anger.
Paul does not believe Christians are sinless or perfect; but he does think they are on a path of seeking God, of being open to God, of seeing the face of God in Jesus Christ.
Tom Wright has an important warning here; Paul does not give us a list of things so we can assess ourselves or (worse yet) others. “What we are not encouraged to do is to draw up a checklist of things done and not done, to weigh them against one another and thereby to arrive at the final verdict” (440).
Overall, then, as we see in vv. 9-10, the final judgment assesse whether a person is “evil” (2:9) or “good” (2:10). The evil are the self-seekers (who do not seek God) and the good are the God-seekers.