According to one reader, "There are so many reasons the Alamodome, in my hometown of San Antonio, is awful ... But most of all, it is deeply, inscrutably ugly, with four gigantic pillars hoisting up the domed roof and making the thing look like a dead armadillo."
Dishonorable mention: The Tobin Center for the Performing Arts in San Antonio
I think a few on the list (slideshow) are actually beautiful.
I think Minnesota has the ugliest by far...