The beginning of the passage recited upon bringing the first fruits to Jerusalem is "ארמי אובד אבי Arami oved avi". The question with which the commentators deal is who was this Aramean and what is this phrase saying about him.
Rashi quotes the Sifrei, which is familiar to us from the Passover Haggadah, that the Aramean was Lavan and "oved avi" means that Lavan the Aramean tried to destroy our father Ya'akov.
Ibn Ezra strongly contests this approach for contextual and grammatical reason. In terms of context, he asks what Ya'akov's going down to Egypt years later has to do with Lavan. Ya'akov left Lavan, settled down, and then some 20 years later went to Egypt. (Rashi's supercommentaries defend him on this point.)
Grammatically, Ibn Ezra points out that the word oved is an intransitive verb. For Rashi's explanation to be viable, the verb should have been in the form of me'abed or ma'avid.
Therefore, commentators other than Rashi offer different explanations of who the Aramean was. Ibn Ezra suggests that it was Ya'akov and oved means that he was perishing -- poor -- in Aram.
Rashbam suggests that it refers to Avraham and oved means that he was wandering. Hence the translation "A wandering Aramean was my father." Seforno takes a middle position between Rashbam and Ibn Ezra, suggesting that the father was Ya'akov but that he, too, can be considered to have been wandering. More recently, R. Elchanan Samet (Iyunim Be-Parashos Ha-Shavu'a, series 1 vol. 2 p. 391 n. 19) states simply that Rashi's explanation is not peshat.
However, R. Wolf Heidenheim, the famous 18th century grammarian, defends Rashi on grammatical grounds in his Havanas Ha-Mikra, cited briefly by Nechama Leibowitz and quoted extensively by R. Ya'akov Tzvi Mecklenburg in his Ha-Kesav Ve-Ha-Kabbalah. R. Heidenheim shows that the form of the word oved can mean continuous action in the past. For example, "And Devorah judged (shofetah) Israel at the time" (Judges 5:4) and "And Pharaoh dreamed (cholem)" (Gen. 41:1). He also points out that there is a similar use of verbs in Arabic. Therefore, he states that the true peshat is according to Rashi and the Sifrei.
It is worth noting that R. Ya'akov Kamenetsky, no slouch in Hebrew grammar, accepts Rashi's explanation. I wonder what Mendelssohn' Bi'ur says on this. I'd greatly appreciate it if anyone with access to it could post a summary in the comments.
UPDATE: I looked up the JPS Commentary (Tigay) and it does not even mention Rashi's explanation. It translates "oved" as either fugitive, perish or stray. It says:
Whichever of these interpretations is correct, it is clear that the Recitation means to contrast the homeless, landless beginnings of the Israelites with their present possession of a fertile land.I also looked up Mendlessohn's Bi'ur. It quotes Ibn Ezra and argues on his translation of oved. It then quotes Rashbam, accepts his translation of "oved" as wandering, but suggests that "avi" refers to both Avraham and Ya'akov.