Often it starts with mutual respect. They recognize each other's abilities and dedication to justice. For instance, Superman respects Batman's ability to fight crime without powers, and Batman respects Superman's selfless use of his powers.
One possible reason could be mind control. Maybe some villain has taken over Superman's mind and made him do it. Another reason might be a fundamental difference in their ideologies that has escalated to the point of no return.
There are quite a few great ones. 'Soulbound' is a popular one where their connection is explored on a deeper, almost spiritual level. It shows how their different ideologies can complement each other in a soulmate relationship.
One of the top stories is 'The Dark Knight Returns'. In this, an older Batman comes out of retirement in a gritty, dystopian Gotham. His return also brings him into conflict with Superman, who is sort of a government - controlled enforcer at that point. It's a great exploration of their ideologies and a very different take on the characters compared to the more traditional portrayals.
Lois Lane is often a popular character. In fanfiction, she might play a crucial role in mediating between Batman and Superman or getting involved in their adventures in a more hands - on way, using her investigative journalism skills.
Alfred Pennyworth is quite popular too. He can offer his wisdom and support to Batman, and his interactions with Superman can be both humorous and heartwarming. He's like the glue that holds things together in the Batcave, and his presence can bring a sense of home to the story.
The worth of the world's finest comic books can be substantial. Factors like the comic's age, rarity, popularity of the characters, and the quality of preservation all play a role in determining its monetary value. Some can fetch astronomical prices at auctions or in the collector's market.