…and how you read them. Please list only the ones that you read regularly.
The New York Times (Website) - Free Portion and Paid Subscription (Times Select)
The Wall Street Journal (Print) - Paid Subscription from work
The New Yorker (Website) - Free Portion
The Atlantic Monthly (Print) - Paid Subscription
Newsweek (Print) - Paid Subscription
The Telegraph - it’s what the have as the ‘quality’ newspaper at my local. I skim the whole thing, then do the crossword.
The Guardian - it’s what I buy when I do buy, and read it properly whenever I visit my parents. News reporting is typical of all the broadsheets, however the G2 fun stuff has become really tedious and dare-i-say-it boring. Steve Bell is still a genius, though.
The Independent - which has a less self-important attitude of indecision 
Paper copies:
Newspapers:
Tampa Tribune. Headlines, national news, commentary, comics, sports.
Magazines:
Popular Photography
Outdoor Photographer
Discover
Scientific American
Skeptical Inquirer
Sci Fi
CFQ
National Review
Combat Handguns
Soldier of Fortune
Black Belt
Online editions:
Newspapers:
Ft Lauderdale Sun-Sentinel. Sports section.
Magazines:
Pro Football Weekly
on a daily basis -
the New York Times
the NY Daily News & the NY Post (mostly just skim these two during lunch-time)
On an infrequent basis -
Newsweek
the Advocate
Out Magazine
Utne Reader
the Nation
Newspapers:
The Standard-Times, daily newspaper covering our area
The Advocate(not that one), weekly newspaper in my town
The Neighborhood News, ditto
The Wanderer, weekly published in adjacent town
Magazines:
Southcoast INSIDER, free regional monthly
SoCo, ditto
Navigator, our town’s free monthly
Smithsonian, subscription
Entertainment Weekly, subscription
Muzzleloader, subscription, (we’re historical re-enactors)
Highlights, subscription (we have a five year old)
My Big Backyard, ditto
Printed Newspapers:
Houston Chronicle
Houston Press
On-line:
Yahoo News
Philadelphia Enquirer
Magazines (all printed):
Aeroplane Monthly
Air International
Car
Car & Driver
Empire
Fortean Times
Offshore
Oil & Gas Journal
Scientific American
Smithsonian
Smithsonian Air & Space
Trains
Newspaper:
Lexington Herald-Leader about once a week.
Kentucky Kernel daily.
Magazines:
Nothing regularly, but I usually take a look at ESPN the Magazine, Sports Illustrated, Time and Rolling Stone when I get a chance.
Most of my news comes from Google News, FARK and Slashdot.
Newspapers:
Akron Beacon Journal (comics only)
Magazines (print):
Wired
Cosmopolitain
They put magazines on the interweb now? huh.
Newspapers:
LA Times (print)
NY Times (Internet)
Magazines:
Smithsonian
National Geographic
Economist
Runner’s World
Sports Illustrated
FourFourTwo
Newspapers:
Uh, does the Onion count?
Magazines:
Discover
Economist
Testosterone
I don’t read any of these super-regularly, just whenever basically:
Newspapers:
St. Louis Post-Dispatch
The Maneater (campus newspaper)
Misery Weekly (campus ‘joke’ paper, really funny)
USA Today (I like the pretty colors)
Magazines:
Spin
Rolling Stone
Popular Photography
And I’m getting a New Yorker subscription (split with roommate) when I get an apartment in August.