We got away from the OP’s request of positive moments into general great moments – there has been a lot of great coverage of not so great events.
For positive, I’ve got a few:
The ultimate release of the mainly American hostages from a hijacked TWA airliner in the summer of 1985. One Navy Seal was killed, Robert Dean Steatham, but all of the other hostages were released mostly unharmed. Thanks to the coverage of the then-fledgling CNN, I will never forget Steatham’s name.
The rescue of Baby Jessica, who fell down a backyard well in Texas.
The Live Aid concerts that same summer, brought to us in the states by the also fledgling MTV. Twenty hours of live, bi-continental music coverage; such an event had never been undertaken nor televised up to that point.
The return of the US to space after the Challenger disaster. We were all on pins and needles until that shuttle was up and away, and I think everyone watching breathed a simultaneous sigh of relief, including Tom Brokaw, who said something to the effect of “I’ve never held my breath for quite so long.”
Televised coverage of Reagan’s 1986 (I think) speech from Germany which included the admonition: “Mr. Gorbachev, tear down that wall!” Most Americans agreed that the Berlin Wall should come down, whether they agreed with Reagan’s politics or not. His demand was impassioned, emphatic and absolutely riveting.
“I knew Jack Kennedy, and sir, let me tell you, you’re no Jack Kennedy.” Now, the positivity of that statement may be open to debate, but I count it as a good moment because it remains one of the single most honest and forthright statements ever made by a candidate for national office.
At the 1996 Summer Olympics there were two moments, first when Muhammed Ali, clearly debilitated of body but resolute of spirit, lit the torch in the stadium. The second was Keri Strug’s triumphant vault, performed while injured and clearly in pain.
The 1980 Winter Games gave us the incomparable moment that the US Hockey Team won the Gold. I can still hear the announced screaming, elatedly, “USA wins! USA wins!”
All three exemplify everything good about sport, never giving up, exceling through seemingly unsurmountable obstacles, and giving your all for the glory of the team and, in the case of the Olympics, the country. Good stuff, that.