Draupadi (1st Wife)
While in hiding, the Pandavas reached Panchala Kingdom it was then Arjuna & Draupadi’s marriage happened. Draupadi was the princess of Panchala and the youngest daughter of King Drupada who was born from the Yajna Agni (Sacrificial Fire). It was said that Drupada wanted her daughter only to be married to the 3rd Pandava - Arjuna. So he had kept the hardest challenge in her Svayamvara so that the most talented archer (which was indeed Arjuna at that time) can only win. In her Svayamvara, Arjuna won her and later she became the common wife of the Pandavas as per Kunti’s order. Arjuna & Draupadi’s love story is a topic of debate in the whole Mahabharata. Some says Arjuna loved Subhadra most, some says Bhima loved Draupadi most. But if one follows the original Vyasa Mahabharata he / she will definitely understand that it was Arjuna and Draupadi who loved each other the most. Vyasa didn’t mention directly but it is the story and small accounts that prove their extreme love for each other.
Uloopi (2nd Wife)
In his 12 years of exile after marriage to Draupadi, when he went to a place (said to be now Haridwar), he met Uloopi - a widow and childless Naga Princess who hailed from the underwater kingdom of serpents in Ganga River. She saw him bathing and became infatuated with him. She kind of kidnapped him and took him to her place. She desired to get intimate with him. Arjuna rejected initially because of his vow of celibacy. It is also said that she told Arjuna that if he doesn’t accepts her she will commit suicide. Later Arjuna agreed and in future they both had a son called Iravan. Many consider it as an “affair” but scholars state their union is legitimized through what is traditionally identified as a Gandharva Marriage - a private, mutual agreement without formal rituals.
Chitrangada (3rd Wife)
After leaving Uloopi’s place Arjuna travelled towards the kingdom of Manipura (not the Indian State of now) and there he met Chitrangada - the princess of Manipura (there isn’t much story on how Arjuna met Chitrangada). They married on a condition that - Chitrangada’s son will be the future ruler of Manipura as the king had not any son. Arjuna stayed there for 3 years and after they got a son named - Babruvahana, Arjuna left the place and started his journey again.
Subhadra (4th Wife)
There are different kind of stories about Subhadra’s marriage to Arjuna. After leaving Manipura, Arjuna came to Prabhasa. When Krishna came to know about this he met him and invited him to Dwarka. Arjuna comes there and meets Subhadra. Some versions say that Arjuna was attracted towards her seeing her beauty and abducted her, some says that it was a mutual decision of both of them where Krishna helped. But ultimately after that they get married in a grand ceremony and Arjuna spends his remaining pilgrimage years in Dwarka. Later he took her with him in Indraprastha.