Another interesting route from LaGuardia is a taxi to 61st St./Woodside, and then LIRR to Penn Station. (Just don't expect the cab driver to become your best buddy.)

The limited-stop train to JFK was called the "JFK Express" or the "Train to the Plane". It started at 57th St. & 6th Ave on the B-train line, made several stops in Manhattan, and at Hoyt-Schemerhorn in Brooklyn, and then non-stop to JFK on the A-train line. I could never understand how they dove-tailed this in with the regular trains, since only part of the route has a separate express track.