MIDWEST DESTINATIONS (IOWA,
WISCONSIN, DAKOTAS, ETC) - American Airlines or United Airlines though
Chicago O'Hare (ORD) or Delta Airlines though Detroit (DTW). Delta has
drasticaly reduced its hub operations at Cincinnati (CVG) after the
Northwest merger but there are still many local midwest connections
through CVG and, though expensive, many more through DTW which was
picked up from Northwest. Delta also operates a smaller hub at MSP but
in most cases you will do better connecting through DTW. Also
consider that Southwest is offering some service through
Chicago Midway (MDW) and Milwaukee (MKE).
SOUTHEAST DESTINATIONS (CAROLINAS, MISSISSIPPI, ALABAMA, ETC) - US Airways (now part of American) through Charlotte (CLT), Delta through Atlanta (ATL). Miami (MIA) is American's Southeast hub (and a large one) but it is usually not practical to fly to the bottom corner of the continent, for flights going inland. If you prefer to fly American and are headed to the Southeast, go through DFW or JFK. Airtran also maintains its hub at Atlanta Hartsfield (ATL)
LATIN AMERICA, CARIBBEAN, SOUTH AMERICA - American Airlines through Miami (MIA), Continental Airlines through Houston (IAH) or Delta Airlines through Atlanta Hartsfield (ATL). And yes, Delta, we know that you can really connect anywhere through Hartsfield!
SOUTHWEST DESTINATIONS - American Airlines through Dallas/Ft Worth (DFW), US Airways (now AA) or Southwest Airlines though Las Vegas (LAS), Delta through Salt Lake City (SLC) or United Airlines or Frontier Airlines through Denver (DEN).
CALIFORNIA DESTINATIONS - American Airlines, Delta or JetBlue through Los Angeles (LAX). United Airlines through SFO (or to a lesser degree, through LAX).
ASIA - Fly though Toronto (YYZ), Seattle (SEA), Portland (PDX) which by the way is a very well liked airport if the route works for you, Los Angeles (LAX), Chicago (ORD), San Francisco (SFO) or sometimes New York (JFK). With Hainan and Japan Airlines now flying out of Boston, you could also skip the connection and get right to Asia from Logan.
EUROPE - You do not need to connect in the US to get to Europe. Logan Airport has flights to London, Paris, Amsterdam (one of the best connection airports in the world, in this writers opinion, other than Singapore), Madrid, Munich, Frankfurt, Dublin, and Reykjavik.
Expect to see some direct flights to Europe emerge via low cost carriers as well beginning with several flights via newcomer Norwegian Air Shuttle.
Dallas original airport is named Love Field (DAL). In the seventies, as air travel was expanding, it was felt that Love Field would not be able to handle the air traffic for the large Dallas/Ft Worth metropolis which is home to more than six million people. So the quest was out to build a new airport which could handle the expansion and thus came the birth of Dallas/Ft. Worth International Airport (DFW) which also became the home and largest hub for the gigantic American Airlines. Airlines were all to support the new airport, but Southwest did not want to move because they liked Love's location closer to where people lived (at the time). So, Southwest (and also Braniff airines) stayed at Love Field. However, Dallas wanted full support for DFW and didn't want to have to operate a smaller airport that was not in full use, so Ft. Worth Congressman Jim Wright, in 1979, wrote the WRIGHT AMMENDMENT which restricted flights out of Dallas Love Field to either Texas destinations or to one of the four adjacent states. The Wright Ammendment helped DFW to grow to the monolith that it is today as the eighth busiest airport in the world according to passenger traffic (and number four if you count aircraft movements since DFW is a very large cargo hub as well). But the restriction also crippled Southwest's business out of DAL and has been a source of debate and controversy ever since.
The Wright Ammendment has in principle been repealed but the changes will not take affect until 2014, before which time there is still plenty of room to reopen the controversy.