I've wondered the same thing myself and have done many searches using various phrases such as "photo album" "gallery", etc.
It seems that the two most popular are Coppermine and Exhibit.
I just uploaded and installed Coppermine and am looking at the psnGallery2 add-on to integrate it into WP. I have to be honest in that first glance at the read me on Gallery2 kind of leaves me a little less enthusiastic about adding it to Coppermine.
I'm curious too if anyone has any links to a "how to" on customizing Coppermine to make it appear like a person's blog? In the meantime I'll do some sluething to see if Coppermine has a forum.
Oh, I had no problems at all installing Coppermine and I've used 4images on my personal non-blog site for over a year. But, just never really liked 4images that well. Although, at first glance Copper kind of reminds me of 4images.