I almost always write in past tense unless I have a compelling reason to go with something else. I think I may have written one short story, years ago, in present tense. I'm a genre writer though, so things might be different these days in literary fiction.
There is definitely no "right" tense and each has their pros and cons, but I would definitely not call present tense the standard. If anything, historically, past tense has been the standard form. It's more natural in the sense that when people tell real-life stories in person, they're telling you about events that have already happened. I don't have the stats here but I'd say that the vast majority of books ever written were all in past tense.