Many interpret it in light of the rest of the larger section, Romans 9-11, which indicates that Paul's language of election is about Jews and Gentiles. In fact, cutting off that section at verse 23 is quite artificial, and even the Reformed-leaning ESV translation groups 9:1-29 into a single pericope. On this interpretation, election is not a choice by God of an individual for salvation but of a group. Arminians believe that God elected the Church, but that he did not preordain exactly which individuals would compose the Church.
Others (myself included) interpret election as a primarily missional term, not a primarily salvific one. This, too, takes into account Paul's assertion of Israel as the original elect and interprets that as a restatement of the covenant in Genesis 12, in which Israel was appointed as the nation through whom "all the families of the earth will be blessed." The elect, then, are not the only people who will be saved, but rather are the people through whom God will work to bring about the salvation of many (or, to some interpreters, of all).
Sources for further reading:
N.T. Wright - Justificiation, Paul and the Faithfulness of God, and other writings. (This blog post has some relevant excerpts from PFG). Justification is part of a larger dialogue with John Piper, so I recommend that book if you're looking for something that specifically addresses the claims of neo-Calvinism.
Douglas J. Moo - The Epistle to the Romans (New International Commentary on the New Testament series). Moo provides one of the most comprehensive catalogues of the various views held on this passage.
Corporate Election on Wikipedia.