Romans 7:14-25 is one of the more controversial passages in the New Testament. Lots of scholars have suggested lots of different interpretations of it, mainly because they find it difficult to see how Paul's emphasis on struggle in the passage fits with what he says in the verses around it.
People seize on verse 14, for example, and say that Paul's describes himself as being sold as a slave to sin, so conclude that he can't really be talking about himself; he must be using “I” to talk about Jews under the law, or something like that. On the other hand, some people read verse 22, and see that Paul says he delights in God's law in his inner being, which is a very Christian thing to say, so conclude that Paul must be talking about himself in this passage.
Lots of people seem to take the approach “my explanation fits this bit, so it's right”. Actually, that's a silly way to look at it. A much better way to try to understand a passage is to say “if my explanation doesn't explain the whole passage, it's wrong”.
If we are going to say who this passage is about, we need something that fits both v14 and v22, and explains why Paul uses the word “I” to describe them.
The obvious answer, of course, is that Paul is talking about himself. Roman Christians wouldn't have read this letter and thought “ah yes, Paul is using 'I' to describe the archetypal Jew living under the law but with an awakened awareness of the gospel”. They'd have thought “yeah, that's what it's like for me too sometimes”.
And it's clear from elsewhere in Paul's writing that he does see the Christian life as a struggle between the flesh and the sinful nature. Perhaps the clearest other place is Galatians 5:17. That also explains the “I”.
For the desires of the flesh are against the Spirit, and the desires of the Spirit are against the flesh, for these are opposed to each other, to keep you from doing the things you want to do.
Galatians 5:17, ESV
So how does that fit with being a slave to sin? Verse 25 is very helpful:
So then, I myself serve the law of God with my mind, but with my flesh I serve the law of sin.
Romans 7:25, ESV
Paul is talking about himself, specifically himself and his sinful nature (“flesh” in the ESV). So in verse 18 he can say
I know that nothing good dwells in me, that is, in my flesh.
Romans 7:18, ESV
So Paul is describing the struggle that goes on in himself with his sinful nature. He describes both himself and his sinful nature as “I”, and even draws a distinction between them in v20.
How does this fit with what Paul says elsewhere? In Romans 7:5 and 8:9, Paul says that the Christian is in the Spirit, not in the sinful nature. I therefore suggest the following summary of the Christian's relation to the sinful nature.
The sinful nature lives in the Christian, but the Christian does not live in the sinful nature.
In other words, sin is beaten in the Christian, but it is still there. It is neither dominant nor absent.