There are a few magazines that I've noticed I read from beginning to end. The New Yorker is one... and another is, Entertainment Weekly! Wow, EW (worst acronym ever?) is such a content-rich magazine. I'm just so impressed by it.
I also tend to read New York magazine from cover to cover. Harper's and the Atlantic I will start at the beginning, but I usually skip over an article or two. It's not in the same class, I think.
What magazines do you read completely from start to finish?