The thing I like about Batman is just that he's human. Not an alien, not an elf, nor cyborg, nor god, nor gelatinous cube. Yet Batman can still face these other creatures and can often defeat them. To me, it is reassuring (even if it is in a highly unlikely fantasy setting) to know a story where the mortal managed to defeat godly enemies or save godly allies. Even if it's through luck, technobullplop, or generous guesses at what a human can do from the writer, but it gives me a glimmer of hope that I can deal with things that seem impossible to me.

I also find the flexibility of interpreting Batman to be entertaining. You can see him as a vaguely benevolent psycho like Nolan or Miller, or see him as an honest person who does what's right even when it is blatantly ridiculous like in the 60s show or The Brave and the Bold. It's just fun to see how many answers people have to the question of: "How does a dude in a bat costume fight crime?"