Arjuna won Draupadi's hand in swayamvar but she was married to all of the 5 brothers .
Arjuna is not happy that he has to share his wife with all the brothers, so he finds peace with Subhadra, Krishna's sister. He favors Subhadra which discomforts Draupadi. She always favors Partha, the archer, the hitman who slays all warriors with a blink of his Gandiva. But alas, Arjuna is busy in his romantic ventures with Subhadra, Ulupi, Chitrangada his other wifes.

This causes Draupadi to have a soft corner for another archer, Karna (pls read the story of Karna And Draupadi). It is said that she secretly adored him but at the same time, she was faithful to her 5 husbands.

Draupadi ignores a man who loved her the most Bheema. Of all her husbands, he is the one who loves her the most. He fulfills her every request, he cannot bear to see her hurt.
Who brings her flowers from Kuber's garden? Bheema.
Who cries because his beautiful wife will have to serve as a maid to queen Sudeshna? Bheema.
Who kills 100 Kauravas to avenge the insult of Draupadi? Bheema.
Who does Draupadi run to when she is molested by Keechak in Matsya kingdom? Bheema.
Who carries Draupadi in his arms because she can't walk in a dense jungle? Bheema

The other Pandavas are not under Draupadi's thumb. She is prone to outbursts of rage, she makes unreasonable, unwise demands. Arjuna is ignorant on her and concentrates on gaining more power from the gods. Nakula and Sahadeva are nothing but devoted to Yudhisitira, they follow whatever their elder brother says. When she wants Keechak killed for molesting her, Yudhisthir tells her that it would expose their presence in Matsya kingdom, and advises her to "live with it" (Model husband that). Bheema simply walks up to Keechak in the middle of the night and tears him limb from limb. No questions asked.

Draupadi shows us Bhima's human side. He is a savage monster with others, but he is always and only tender when it comes to Draupadi.

We all know what happened in the infamous dice game. Dussasana tried to disrobe her but fails (thanks to Krishna). Bheema walks up to the center of the court room and makes a vow

"I, pavan putra Bheema, husband of Panchali pledge that unless I drink the blood of Dushashana and break Duryodhana's thigh, I will not show my face to my ancestors"
Jayadratha, Duryodhana's brother in law, tried to abduct Draupadi in the forest and she was rescued by Bheema. Bheema almost killed Jayadratha but Draupadi said that he is the husband of Dusshala, Duryodhana's sister and hence your sister too. Don't kill him.

Bheema took a vow that he would slay all the 100 Kauravas. In the 14th day of the battle, he drinks blood from Dushashana's chest, carries the blood and runs to Draupadi. He sprays that blood on her hair and fulfills his pledge. Only after this, Draupadi ties her hair after 15 long years.

Draupadi was the first to fall when Pandavas were on their final journey to heaven. Soon after Draupadi, Arjuna, Bheema, Nakul and Sahadeva followed. It is said that Bheema crawled up to Draupadi and accompanied her while she was breathing her last.
Bheema had said -
"O my queen, what can I do for you?"
Draupadi had replied -
"O my beloved husband Pavan Putra Bheema, you are the only one who have given me all that a woman longs for. But I have been ignorant towards you. I have been blind for Partha but you have protected me every single time and repaid me for the humiliation I had received. In our next birth, be the eldest."

She weeps and dies in the arms of Bheema.