This is part of a larger project reviewing commentaries on each book of the Bible. Follow the links from that post for more information on the series, including explanations of what I mean by some of the terms and abbreviations in this post. This is not an exhaustive list, just the commentaries that I think are most worth paying attention to.
Pride of place goes to the NIGTC volume on I Corinthians by Anthony Thiselton (2000). This is now the most in-depth recent commentary on this book. It's based on the Greek text, and it includes a number of long excurses on difficult issues, so this isn't an easy read, but it's not mainly the Greek that's the issue. It's just a very dense, scholarly work, and it's hard to capture that in popular-level writing (although I think Thiselton is clearer most of the time than most academics are). Thiselton gives close attention to the Greek lexical and grammatical issues, the social background of the letter, Paul's rhetoric, and other elements commonly found in commentaries. Thiselton is also an expert in hermeneutics. One unsual thing about this commentary is that he also includes a lot more of the history of interpretation than is typical, since one of his strengths is the history of theology. I've read some lengthy enough sections of it to know that it's tough-going if you're not up on your Greek, and the excursus I read (on gender issues) was so detailed that it was difficult to get a clear sense of what Thiselton's conclusions amount to. The wealth of information and close attention to detail make it an excellent resource for consultation, even if it might be more difficult to read the whole book cover-to-cover the way I like to. I expect this to be an important scholarly standard for some time, even if Ellis has a good chance of eventually take that place (see forthcoming commentaries below). I also very much appreciate Thiselton's application of speech-act theory (from my own field of philosophy) in biblical studies. Thiselton's philosophical background also makes him more trustworthy on the moral philosophical background of the Greco-Roman world.
David Garland's BECNT (2003) is very good. I've looked at it less than I have some of the other volumes here, but it was enough to see that this is now the first place to look for a more readable treatment than Thiselton. Garland is widely respected by scholars across the spectrum. He left a Southern Baptist seminary because of his egalitarian stance, but on most other issues he's fairly conservative. He has ten years of additional scholarship to influence him and to respond to when compared with Fee below. Fee has such a high reputation that it was difficult to put Garland ahead, but I think I'd actually give up Fee if I were forced to choose. Garland's NAC on II Corinthians was very good, and I think this BECNT is even better. He's also done work on Matthew and the NIVAC volumes on Mark and Colossians/Philemon. He's currently contracted to write commentaries on Luke (ZEC) and Thessalonians (NCC).
Gordon Fee's NICNT (1987) was for a long time the commentary to buy on I Corinthians, but Garland and Thiselton have interacted with a lot of recent scholarship since Fee's commentary was published, and they are at least as good on enough issues that I recommend them slightly higher than Fee. I would prefer not to be without any of them, however. Fee is an excellent commentator in so many ways, including matters of language, historical and cultural background, flow of the argument, and textual criticism. But this very scholarly work doesn't come across as mere scholarship but as the work of someone with a vital relationship with God thinking through the scriptures in a way that will be profitable for his audience. He ends each section with contemporary application issues, but even throughout the commentary you'll frequently find him passionately engaging with Paul's thought or reflecting on the relevance for daily life of the principles he derives from Paul's letter. Fee is one of the most respected Pauline scholars of our time, having now written or planning to write commentaries on Galatians (PC), Philippians (NICNT), Thessalonians (NICNT), and the Pastoral Epistles (NIBC), along with a Pauline theology of the Holy Spirit and an excellent NT Christology. [He's planning Revelation for NCC, so he'll finally be verging into something outside the Pauline corpus.] Most people consider him a moderate Pentecostal. His views are actually not too far from some Reformed charismatics and non-cessationist non-charismatics. I wish most Pentecostals would read this commentary or God's Empowering Spirit to see how someone can be Pentecostal without flatly contradicting scripture in their practice of the so-called sign gifts. One of Fee's most controversial moves in this commentary is his rejection all of the egalitarian approaches toward I Cor 14 as exegetically impossible, leading him to conclude, against all evidence, that the short passage in question is an interpolation by another author despite its being in every manuscript.