When leaving home, I usually start with that day's newspaper(s), then any older newspaper sections I haven't read (usually day before or Sunday special sections). Then I move on to a stack of magazines, starting with the time-sensitive ones, such as Sports Illustrated. I usually pack in my checked luggage a few evergreen magazines, such as travel mags or alumni mags, for the flight back. Depending on flight length I may carry these on board.

For a really long trip I'll bring a book as backup material.

Flights are a great time for me to get rid of my backlog of reading material. As you can probably figure, I ditch everything on the plane, although often other passengers or FAs will take my reading material for themselves (fine with me!).