Like Eddie said, the Apollo-Soyuz Test Project, the first international manned space flight.

International Space Station Flight 2R, the beginning of human habitation on the ISS.
{Edit}
On second thought, that wasn't a NASA mission.
So I'll say STS-88, first shuttle flight and beginning of the ISS assmebly. Zarya was previously launched on a Proton rocket, and the (I think) Endeavour carried the Unity module up and attached them.
{Edit}

Wetzel
~~~~~~~~~~~~~~~
Soyuz-Apollo for you Russians out there
:rolleyes:

i voted apollo 13 (no, not because there's a movie about it)...there is no other mission that showed the true resilience of the NASA program

Not to mention the resilence of the contractors who made the equipment (the guys from Grumman did flip...that's what I understood...and my dad works for Grummman well Northrop Grumman now). But its also reflects the challenges of engineering and the determination of NASA to bring their people home safely.

I'm going to have to say Apollo 11 because it triggered a whole new way of life. I think that if that mission had failed, space travel all together may have been put on hold.

I'd think we'd try again and again to get it right.

Well, Nixon did have a big address planned in case the astronauts didn't make it home.

Yeah, just like he had like for election...gave the US what they wanted and started Vietnamization in Vietnam to bring troops. He said he had a plan and really didn't...but he patted his breast pocket of his jacket like he did. So did he really....besides the press secretary probably wrote it anyway.