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.
Gordon Wenham's WBC (1987, 1994) receives the best all-around reviews of any commentary on Genesis and from a wide range of people. Wenham is a moderate to conservative evangelical. He spends some time on source-critical issues, generally taking a skeptical stance toward those who think they can delineate sources and identify different time periods for different parts of the book. Wenham is good at historical background, often defending the plausibility of the narratives, particularly in the patriarchal section. He spends more time than most academic commentaries dealing with matters of theology and even Christian application. Of the Genesis commentaries that are accessible enough for someone like me (i.e. someone not knowing any Hebrew) to read, Wenham's is the most detailed on textual criticism. One strength is his proportionally-greater treatment of the structure of individual passages, although some might think it's a bit much. I did think the commentary was a bit briefer than I expected once you get through the literary and source-critical issues. His structural analysis shows a tightly-woven narrative by a single mind, which undermines the credence he shows to the general source-critical approach (as skeptical as he is of particular proposals in source criticism). Wenham has an absolutely stellar NICOT on Leviticus and a pretty good exposition in TOTC on Numbers. He also has done a lot of more general work on the Pentateuch and is generally seen as one of the top Pentateuch scholars of our time.
Victor Hamilton's NICOT (1990, 1995) is about at the same level. He is a conservative evangelical, and the series is generally seen as being more conservative than WBC, which is probably the reason he gets a little less attention from the less-conservative end of scholarship. I think the commentaries are about equivalent in quality, with Wenham perhaps winning out a little more often in terms of incisive exegesis but Hamilton giving a little more depth on more issues, especially in his introduction. Hamilton is particularly better on linguistic issues such as grammar and close analysis of particular words, but I think he may sometimes overdo it chasing lexical rabbit trails, and he's perhaps less strong on big-picture thinking. He takes the time throughout his commentary to look at the New Testament use of Genesis. I would say that Hamilton and Wenham balance each other pretty well as a pair. Hamilton is also known for his Handbook on the Pentateuch.
Bruce Waltke had a set of exegetical notes he would distribute to his Genesis seminary classes, and one of his former students, Cathi J. Fredericks, talked him into letting her edit them for publication in this 2001 volume. He did expand on them in places, but these are mostly brief exegetical notes with theological summaries for each unit he discusses. I generally find his exegesis to be the best of any of the Genesis commentaries I've looked at, but there isn't a lot of detail here on historical background, language, and many other things you might expect to look to a commentary to help you understand. The book is uneven, having much more discussion on the parts he chose to expand on and much less of insight on the notes he chose to leave as they were. It makes it hard to tell the intended audience also, since it doesn't have enough depth on every matter for academic work, has a bit much on structural and rhetorical elements for the average paster, and isn't evenly balanced in amount of detail across the whole book to be a first choice for any purpose. Nevertheless, I recommend it with Hamilton and Wenham as an excellent supplement to their more detailed work. Waltke is a conservative evangelical, and he's also known for excellent commentaries on Proverbs (NICOT) and Micah (Eerdmans) as well as an oft-cited Hebrew grammar.