Krishna aside, the contenders for the next spot include Arjuna, Krishna, Bhishma, and maybe a few others. Some might even put Duryodhana in their list. I, however, put Bhima on top.
Bhima is born the second son of Pandu and Kunti (an avatar of Vayu). Even as a child, his immense strength is on display. When the Pandava children are playing, Bhima is accidentally dropped on a rock. To the parents' surprise, it is the rock that is shattered and Bhima is as cheerful as ever.
During the training period under Dronacharya, along with the Kauravas, while Arjuna chooses the bow and arrow as his weapon of choice, Bhima picks the gada (mace) and so does Duryodhana. (Duryodhana is also actually taught by Balarama, Krishna's elder brother).
In the Draupadi swayamvara, it is Arjuna who is chosen to contest (shooting a revolving fish's eye, not looking directly at it?). While the popular version of the story tells us that 'Arjuna won Draupadi' but due to Kunti's mistake all the brothers end up 'sharing' her, there are other lesser known versions with deeper explanations. One of the back stories is that Draupadi ends up with '5 husbands' because of a wish that was granted by Shiva to her in her previous birth (as Nalayani, the daughter of Nala and Damayanthi). Instead of getting a husband with her 5 favourite qualities, she ends up getting 5 separate husbands. Shiva also blesses her that she would regain her virginity each morning. I have heard another back story that extends this. 4 other devis (the divine consorts of the other Pandavas I think) also have some similar wish granted, due to which they end up having to share Draupadi's body. It is the right devi that actually inhabits Draupadi's body each time 'Draupadi' is with a Pandava.
In any case, Draupadi herself is considered an avatar of Bharati (consort of Vayu), and hence it cannot be Arjuna that is the 'rightful' husband, even though he is the one that participates in the contest. It sure is Bhima. There is a much longer story behind why Arjuna is chosen to contest, and not Bhima. The story involves Shikhandi (something I recently learned of) and will try to post this sometime soon.
Some other quick points on key Bhima acts/slayings:
1) Even in Duryadhana's court, before Draupadi's vastraapaharana took place, Bhima is all fury, and is controlled by Yudhishtira. He makes a vow to Draupadi that he will bring her the blood of Duhsshasana until which Draupadi vows that she will not wash her hair (?). I don't know of any other Pandava
2) Bhima slays Duryodhana and Duhsshasana in the war. These are the main evil characters in the entire Mahabharata.
3) Bhima sacrifices his son Ghatothkacha without a second thought, for the sake of Dharma. Had it not been for Ghatothkacha, Arjuna may have been harmed by Karna. More on this story later.
4) In no way does Bhima ever doubt that Krishna is the supreme being. Arjuna is in doubt whether Krishna might be harmed, forgetting that Krishna is the one controlling the chariot and Arjuna merely the tool. Yudhishtira is afraid that Duryodhana might harm Krisha when he goes to his court to negotiate peace; again forgetting that He protects all, and there should be no such doubts. I am not taking anything away from Arjuna or Yudhishtira, and I am being nitpicky, but these are devatas we are talking about and each one has his/her position in the hierarchy of the pantheon of Gods.