Boston is a focus city for many airlines because of the wealth of traffic coming info and out of the area. However it has never been a true hub for any one airline, probably due to it's location in the Northeast corner of the US and it's proximity to the much larger NY market. However, Jetblue has clearly become the biggest airline in Boston, by a wide margin. In spite of also being a NY airline, with it's hub and home offices in Long Island City, Jetblue has begun to lay it's plan to feed international flights to Europe through Boston.
Fliers to and from Logan Airport who are going to cities not serviced by Logan directly will have to connect in regional hub cities. The following is a suggestion list of major airline hubs and the areas that they often serve:
MIDWEST DESTINATIONS (IOWA, WISCONSIN, DAKOTAS, ETC) - American Airlines or United Airlines though Chicago O'Hare (ORD) or Delta Airlines though Detroit (DTW). Delta has drastically 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. There are quite a few midwest cities though that Delta services directly such as Milwaukee, and Indianapolis. Also consider that Southwest is offering some service through Chicago Midway (MDW) and Milwaukee (MKE).
SOUTHEAST DESTINATIONS (CAROLINAS, MISSISSIPPI, ALABAMA, ETC) - American airlines through Charlotte (CLT), Philadelphia (PHL), 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.
LATIN AMERICA, CARIBBEAN, SOUTH AMERICA - American Airlines through Miami (MIA), United 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), American Airlines 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 and United all fly to Los Angeles (LAX). United and jetBlue fly to SFO. jetBlue, flying almost everywhere from Boston also has some flights to Burbank, San Diego and even Palm Springs. Sadly, jetBlue has exited Long Beach Airport (LGB) as the City of Long Beach is no longer allowing airlines to hold unused gates for further expansion.
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. Cathay Pacific has also offered a flight to Hong Kong, continuing to make the need to connect from Boston a thing of the past. Cathay is part of One World, and is a terrific airline if you are willing to pay for it.
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. I highly recommend skipping connections in JFK and making your first stop on The Continent.