Sam leaps into the body of an ABC network executive in 1986 and changes the decision to not turn the I-Man pilot into a series.
He repeatedly leaps into the life of a mentally disabled man named Forrest Gump to make him vastly more successful than he would have been otherwise. 
He leaps into a production of “The Rocky Horror Picture Show” just as they’re singing “Let’s Do the Timewarp Again”.
Sam can only leap within his own lifetime.
Sam leaps into Waylon Jennings before he gives up his seat on the plane to the Big Bopper.
Broken in the series when he leaps into a distant relative during the Civil War.
Boom… rule broken once…
The cartoon character episode along with the Magnum PI episode sounded like delightfully awful final season ideas.
But they gave a REASON for it to be broken; the soldier was a direct ancestor of Sam’s. It was a weak justification, but it was a justification.
Oh, and I agree that there are a few too many “real life” figures being suggested. Many folks think that there being so many in the last season was a sign of weakness.
One popular fanfic idea is to explore who/what’s behind the Evil Leapers. How about Leaping into a man lost in the woods? It’d be a great place for Leaper/hologram interaction with a lot of tension. A 911 operator? Having to accomplish a mission purely on what you say, not what you do, is interesting; the only way to know anything about what’s going on on the other side of the line is the caller (whose POV may be wrong) or holographic observance. A candidate during a small town mayoral debate? This would be another riff on the “purely what you say, not what you do” thing. A doctor who performs abortions? Could be a very nice conflict of morality setup on multiple levels, even better if it takes place pre-Roe v. Wade. One more: a minor street thug who’s really a confidential informant, and must balance his own life versus the information he can get/give to the cops.
ETA: This show is where I got my nick, so obviously I’ve thought about this quite a bit. The above is pretty much off the top of my head, tho’.
De gustibus and all that, but I remain hugely disappointed in the original QL series finale. And it took, what, a four hour episode to get there?! OK, slight exaggeration, it felt like no more than 180 minutes of crud before we found out that Sam does not get to go home, but he does undo the source of all of his useful knowledge throughout the previous episodes. Al was always married to or dating or screwing around with someone who taught him Hebrew or Urdu or trapeze or whatever it was that Sam needed to know at a critical juncture.
But then Sam made all that didn’t happen :smack: - and in a boring episode. :mad:
But back to the OP and “Quantum Leap - The Next Generation”. I’ve been obsessing about this all day. 
Casting the “Sam” role is tough. For all the complaints about Bakula, he proved to be a very versatile performer in QL. He played men and women, old and young, and multiple ethnicities. He sang, he danced, he was caring one minute and kick-ass the next, all while being very likeable. Whoever plays “Sam” in QL2 has got big shoes to fill IMO.
Creating the “Sam” character is also tough. Sam Becket was an MD and a martial arts expert. Those were very useful attributes during the series. He also sang - again useful in a light entertainment.
I suggest making new “Sam” an MD with a PhD in neuroscience. I see him as the designer and builder of the brain-to-macguffin interface. As an MD he has the knowledge to patch people up in a crisis, or even, for example, get his leapee’s pregnant wife very drunk under doctor’s supervision to stop her pre-term labor before the appropriate drugs were invented. With the PhD in neuroscience he’ll have to know a little bit of everything, so he can be as useful as required in any MacGuyver or Gilligan’s Island Professor situation. Keep martial arts and singing as hobbies, and you’re good for any adventure.
Nostalgia was a huge part of the show’s appeal. According to IMDB, Sam Becket in QL was born on August 8, 1953. The show took place, as I recall in 1999 (ten years after the series started), so Sam was 47. I think in QL2 you’d again want someone about 45 years old. If you make the series in 2010 and set it in 2020, then new Sam would be born around 1975. If you keep the time travel within his lifetime, that gives you some 70s nostalgia, and much 80s and 90s and 00s nostalgia. I don’t think you want to go too heavy into the 70s, what with Lost and Life on Mars, but it depends on what your writers do for you. An episode with the bicentennial as background might be good.
A problem with this time frame is that I don’t think there was as much social change in the 80s-00s as there was in the 50s-70s. I could be wrong. I also think that medicine was better developed, so tricks like the above mentioned ethanol IV Sam pulled out in the premier episode would not require Sam - they’d already be standard medical practice. Well, not necessarily.
With that said, here are some episode ideas:
“Sam” leaps into an Iraq War vet with PTSD. Sam starts getting symptoms, but manages to help the vet and family anyway.
Another war bride story - this time Gulf or Iraq War, and this time she’s Muslim. Sam helps overcome prejudice and keep marriage together. If the bride is a christian, but escaping problems in her home country, that works too. Bigots would reject her regardless.
Sam leaps into an Iman in a town with anti-Muslim prejudice.
Sam helps an anti-gay fire and brimstone preacher reconcile with his gay son or daughter. Sam can be the preacher or the kid, or the Mom, or a straight sibling. I must say here that I didn’t care for leaping around within episodes.
Sam leaps into George Harrison and helps him and his wife defeat the crazed fan who attacked them in their home. This might be too violent for a light TV show.
Sam leaps into a White House guard, or Secret Service Agent, during the Lewinski scandal. Sam’s there to help the leapee with a personal issue, or stop an unrelated crime that is unremarkable to history. The White House is just background.
Sam leaps into a computer tech right before 12/31/1999. Sam’s not there to fix any Y2K problems - the fixes for that had all been done except for watchful waiting. Again, he’s there to fix a non-Y2K personal crisis. The guy’s wife leaving, something like that. You can set this one in New Zealand, since they were the first industrialized country to hit 01/01/00. I remebr waking up the morning of 12/31/99 and checking a message board for Y2k issues; I felt much better when Auckland reported nearly everything was OK.
Sam leaps into the Tiananmen Square protests.
Sam leaps into an early rapper - um, best be one that lives. Or helps a young rapper get his life together, even though rap is not a career for him.
Sam is a doctor during the King riots. Just tweak the Watts riot script from QL1. Unfortunately, we can’t all just get along.
Sam stops a 80s/early 90s computer geek kid from going off with a person she/he “met” on line. In the original timeline the kid disappeared.
That’s enough - I need to leap off to dreamland! The show meant more to me than I thought.
I like this one.
How about one where Sam leaps into the friend/acquaintance of a small-town high school kid in the early 60’s. This kid is popular, successful, good-looking, gregarious, etc…but Al tells Sam that the kid commits suicide in a few days. Sam insists that it isn’t possible, but by the end of the episode it comes out that the kid is gay and that he didn’t know how to deal with it. Sam talks him out of killing himself and helps him cope with his newfound identity.
Isn’t Sam caught in a continuous loop by the end of the last episode? Isn’t the next episode the first episode? At least, that’s what I remember, but I apparently was too young or missed too much of tit to understand some of the plot points mentioned here, so I could be wrong. But, if I’m right, the new series could not involve Sam.
Therefore, there is no reason for us to be so highly tied to the original mythos, anyways. The new leaper will likely be using an advanced version of the system. There’s no reason we’d have to be tied to the leaper’s lifetime. And that’s a good thing, considering that the trend is to cast younger people in roles nowadays.
Assuming all of this, I’d like to see them leap into someone involved in the quantum leap project, giving Bakula a cameo role. Even better would be to revisit some of the leaps Sam already made, but from a different perspective. (You could get a cameo in there, too, by having the new leaper accidentally touch Sam’s character.) Heck, we could even revisit the ending of the first QL.
The new leaper leaps into a very young Don McLean hearing about the plane crash and instead of young Don committing suicide, “American Pie” is born.
1:30 AM, 28 February 1997: Sam leaps into a member of the LAPD. Some eight hours later, at the end of the episode, he suggests borrowing inventory from a North Hollywood gun shop.
17 March 2003: Sam leaps into tobacco protester Dwight Watson as he’s about to drive his John Deere into the pond.
In one of the best Quantum Leaps ever, Sam leaped into a navy cadet suspected of being gay. Al thought he should be drummed out of the navy, but Sam kept saying it didn’t make a difference.
Sam and a closeted teacher talked the kid out of suicide. In the end Al agreed with Sam that the gayness was irrelevant (I changed my mind. Did I ever say I was perfect?). When Al asked Sam at the end if the guy was gay, Sam asked “Does it matter?” and leaped.
Did Sam ever do anything bad or morally ambiguous? The saccharine is what put me off the series.
I don’t know if it was intended to be morally ambiguous, but in one episode he leaps into someone who turns out to be a hitman contracted to murder someone. In the hitman’s place, Sam turns himself in; he basicly gets the guy arrested and convicted of attempted murder. That was Sam’s decision, not his unwitting host’s.
More!
Sam should leap into:
A dot com company. Fooseball and other forms or pointless geek hilarity ensue. Step 3 - Profit!
An Enron-like company. He’s the whistle blower of course.
The breakup of Yugoslavia. This should be a three-parter with Sam leaping into someone from each side at different points.
It might be fun to have Sam leap into a writer for a TV program that is virtually identical to Quantum Leap. The reason for his being there would be unrelated–someone’s personal problem or something–but I’m imagining some really funny scenes where a bunch of the writers and producers are sitting around hashing out show ideas, and Sam is all like “Oh, someone in that situation would never do that!” He could get all adamant and stuff, and cause the people around him to notice that something is a little off about whoever it is that he leaped into.
“Jesus, Frank, when did you become an ‘expert’ on how some guy leaping around through time would feel!?”
And just some food for thought–is there any reason that Sam can’t be a Samantha?
I’d probably do something really mean-spirited, like have him manage to prevent U.S. involvement in Vietnam…and have the next leap be a UN aid official trying to manage the mass exodus of refugees from the Sino-Soviet proxy war consuming southern Asia in the early 70s. Then the third episode would have him undoing that…and then managing to inadvertently get the same UN official murdered in Operation Phoenix, or something.
Sam is a punk rocker!
In that leap, or another one where he’s a performer, Sam leaps into a locally famous performer who is a drug addict. Sam thinks he’s there to get the leapee free of drugs. But he’s not. In fact, Sam is jonesing bad, and breaks down and uses drugs to feed the leapee’s addiction. A younger person - gopher or groupie or whatever - witnesses Sam taking drugs, and Sam gives a nice little “don’t be like me” speech. The kid grows up free of drugs and lives a good, of not famous life. In the original time line both the leapee and the kid died from overdoses. Now it’s just the leapee.