When I was doing a bunch of exegetical work in Romans, I came across Ben Witherington's commentary and read his comments concerning the perplexing language Paul uses in chapter 7. I had always been bothered by the language of 7:7-25 because it seemed quite unPauline and I saw it adopted by pastors in order to experience what a famous scholar said "the introspective conscience of the West" (Stendhal). Instead of Romans 7 being about this modern introspection, Paul was doing something completely different. Believing I had discovered something new (always a bad thing to assume in the work of New Testament scholarship, but hey), I ran to my wife and explained it to her.
A minute later, she nodded and said something to the effect of, "yeah, when I was in undergrad I randomly read a book on ancient rhetoric and Romans 7 fit that. Yup. Its Adam."
So, in order to briefly argue my point, I am going to offer several reasons why I think Paul is using prosopopoeia ("speech-in-character") in Romans 7:14-25. This post is not exhaustive, of course, but it seems to be the best option out of many. Others have proposed Israel as the voice, humanity as a whole, Jews as a whole, Gentiles as a whole, and other Christians who struggle with sin. I suspect it is none of these.
Stanley Stowers (Toward a Rereading of Romans, 16-21 specifically) explains προσωποποιία as "a rhetorical literary technique in which the speaker or writer produces speech that represents not himself or herself but another person or type of character" (pp.16-17). Stowers argues that Romans 2:1-5, 3:1-9, 3:31-4:2 and 7:7-8:2 are best read as προσωποποιία. He also notes that προσωποποιία is often in the first person singular (p.20).
Witherington (hereafter BW3: Paul's Letter to the Romans, 180) states ""Since the important work of W.G. Kümmel on Romans 7, it has become a common, perhaps even majority, opinion in some NT circles that the 'I' of Romans 7 is autobiographical." Given how Paul speaks about the law in Galatians 2:11-14 and Philippians 3:1-11, it seems safe to say he did (or more accurately, "does") not have a major problem with the Jewish law. BW3 rightly then says that this does not tell us "who" the voice of Romans 7 is.
Instead of autobiography, BW3 offers us Adam in Romans 7.
Regarding typology and sequence, one needs to offer some sort of lens or person in which they can speak. The last person Paul has talked about is Adam in Romans 5:12-21—this of course assumes that Paul is not speaking of the inner turmoil of Jesus in Romans 7! For instance, Jesus had the Law—Adam did not. Adam was "separate" (χωρὶς) from the Law (singular: νόμου) in 7:9. However, Adam did have a singular commandment, and it was not the Mosaic Law.
Adam did not know about lust or sin before the Fall (7:7), and because of the primordial couple's sin, Sin came to life (ἀνέζησεν: 7:9)
Second, Sin is personified here as it was in 5:12-21. For instance, ἡ ἁμαρτία ("Sin") is active in "accomplishing" something in Adam (κατειργάσατο) in 7:8 and this Sin kills in 7:11 (ἀπέκτεινεν). It is unlikely that this could be referring to Israel or to Paul or even to the believers, but it makes sense under an Adamic paradigm. The reason why it most probably does not refer to the believer is the comment in 8:1: Οὐδὲν ἄρα νῦν κατάκριμα τοῖς ἐν Χριστῷ Ἰησοῦ ("Now then there is no condemnation to the ones in Christ Jesus").
If one adopts the Adamic reading as opposed to the other readings (which are legion), then one may find themselves identifying with Adam. The purpose of προσωποποιία is for the audience to find themselves in a specific line of dialogue or monologue, to understand the deep contrast between life and death that characterizes Adam and Christ.
7:24: τίς με ῥύσεται ἐκ τοῦ σώματος τοῦ θανάτου τούτου ("Who shall rescue me from this body of Death?") Adam's introduction of Death gave birth to the human condition of Sin. We are born into sin, although whether or not we are guilty of Adam's sin is a concept not apparent in Romans 5-7.
Paul is not speaking about the person's inability to follow the Law, or about your sin, or my sin, or your mother's sin, or anything like that. He is using Adam as a rhetorical device to assert that a former state is now undone. Because one is in Christ, condemnation is now a relic. Having been rescued from the Adamic state of Death and Sin and utter destruction, we now have life in Christ and in the Spirit (c.f. Romans 8:1-11). Adam is the contrast to the new life that we have in Christ.
Christ is bigger than Adam, and Paul's use of προσωποποιία showcases his remarkable rhetoric and his incisive analysis of the ones apart from Christ, destined for death and slavery, and the ἐλευθερόω ("liberation") by Christ from the law of sin and Death (Romans 8:2). Instead of those formerly in Adam being condemned, Sin itself is condemned (κατέκρινε: 8:3) as we walk now in the "Spirit" (πνεῦμα).
Read Romans 7:7-25 with Adamic eyes and see for yourself. There are other options, but given the context and nature of ancient rhetoric, Adam seems to be the best exemplar of Paul's language.