Does NASA ever plan crewed missions without a free return trajectory?

Question

Because the mission was launched on a free return trajectory, the crew of Apollo 13 survived. Has that abort option ever been foregone in any mission that flew or was seriously planned?

(A free return trajectory is one that will allow a ship to return to its origin because it picks up enough speed on a low pass around a second body to escape its gravity and head back home. No fuel is needed to return. The Apollo flights landed instead of heading back by retro-firing their engines to slow down, except for Apollo 13.)

Answer 1

Apollo missions 8, 10, and 11 were free-return trajectories, but this greatly limits the choice of landing sites. From Apollo 12 onward, the initial trajectory was a highly elliptical orbit that did not reach the Moon (technically suborbital: the perigee was inside the Earth's atmosphere); once everything checked out, a mid-course correction was used to put the spacecraft on a non-free-return lunar trajectory.

Answer 2

Apollo 13 was not on a free return trajectory when the explosion happened, in order to target their landing site. They had to execute a 30-second burn of the Lunar Module engine to get on a free return trajectory.

So, yes, it was planned to not be on a free return for much of the Apollo 13 trajectory. So that must count as "ever".

Answer 3

The Apollo missions are the only manned missions thus far to leave Earth's orbit, and as such are the only ones for which a "free return" (to Earth) trajectory has meaning. (As noted by Mark Adler, the Apollos didn't normally fly free-return trajectories, but could easily get on such trajectories.)

For near-Earth missions, a "free return" to Earth means a sub-orbital trajectory (like the first two Mercury missions). Once you're in orbit, you're not in free return (discounting eventual orbital decay from atmospheric drag), but you can return for a very small energy investment.