Did the Pandavas eventually take rebirth? If they did, who were they and what happened to them?
Arjuna was reborn as Kannappa Nayanar, one of the 63 great Shiva-bhaktas in South India. When Arjuna fought with Lord Shiva as a Kirata to obtain the Pasupatastra, he had at first insulted him based on his caste (although later he admired the hunter). And after realising who He really was, Arjuna fell at Mahadeva's feet and repeatedly asked for his grace. Therefore, as a combined result of this, Mahadeva told Arjuna that he will have to take another birth, but will live only for sixteen years. He would perform Shiva-bhakti for six days, and return back to His abode. Thus, Arjuna was born as Kannappa Nayanar.
No Arjun didn't take rebirth. In fact he attained Vaikunta , the highest of all positions . The Mahabharata itself clearly mentions it. In Gita Krishna himself describes that no one is dearer to him as Arjuna. In fact Krishna-Arjun were Nara-Narayana. There is no question of rebirth for Arjuna. The story of Kannappa is different . As per original Mahabharata, Arjuna attained Vishnu Loka
He beheld Govinda endued with his Brahma-form. It resembled that form of his which had been seen before and which, therefore, helped the recognition. Blazing forth in that form of his, he was adorned with celestial weapons, such as the terrible discus and others in their respective embodied forms. He was being adored by the heroic Phalguna, who also was endued with a blazing effulgence. The son of Kunti beheld the slayer of Madhu also in his own form. Those two foremost of Beings, adored by all the gods, beholding Yudhishthira, received him with proper honours.