The core principle for the series was Wilton Knight's belief that "one man can make a difference". In terms of inspiration, that's up there with Peter Parker's maxim about power and responsibility. This set up the "wandering hero" story structure, which ran for four years (1982-1986).
After the series finished, there were a few follow-ups, some of which worked better than others. As far as I can tell, each of them is independent, i.e. the timeline diverged into three separate continuities.
Knight Rider 2000 (1991)
This was a one-off film, intended as a pilot for a new series which never came to be. Honestly, it was a bit disappointing; maybe worth watching if you want to see one final adventure for the original team, but not much good on its own merits.
The basic premise is that time has passed and technology has progressed, so KITT no longer stands out as a supercar anymore. His actual car body has been scrapped and his AI components have been stuck on a shelf. Meanwhile, Michael has retired and he's living a quiet life with a different car. When I saw that, I immediately thought that surely Michael would have been happy to take KITT with him if FLAG didn't want him anymore, rather than abandoning him in a warehouse. Anyway, events bring them both out of retirement, so Michael puts KITT's chips into his own car.
This leads to a very random cameo from James Doohan:
The "mistaken identity" bit is significant to the plot (showing that KITT isn't working properly) and I suppose it helped to have someone that the characters would instantly recognise, but it's still weird. I also can't help thinking that it will irritate actors if you call them by their character's name.
Anyway, the upshot was that KITT got a new body (a "concept car") and a new driver, allowing Michael to go back into retirement.
Team Knight Rider (1997-1998)
Here's the intro:
Quoting from that: "10 years ago, all it took was one man and one car to get the job done. Now, the Foundation for Law and Government has assembled five highly skilled operatives and paired them with the most advanced state of the art vehicles, to take on a new breed of outlaw. They are Team Knight Rider!"
The implication here is that if you're alone then you're completely useless and there's no point even trying to solve problems, so you might as well just go back to bed. That didn't really impress me. It later transpired that KRO (KITT's successor) and his driver went rogue, much like KARR, and killed several people. The five new vehicles were specifically designed to be weaker, so that the rest of the team could stop one of them if necessary.
There was a bit more variety in the new vehicles, including two motorbikes (which could join together to form a car). However, here are pictures of the two bikes: Kat and Plato. These bikes are both enclosed at the sides, probably with doors. If you're used to driving a car then that may not seem like a problem. However, on a bicycle or a motorbike you have to put one foot down on the ground each time you stop (e.g. at a red light). There are a couple of techniques for bicycles, but on a motorbike you have to lean the bike over to one side and then stick your leg out to that side to put your foot down. Looking at the TKR bikes, you can't swing your leg out because some idiot put a big piece of metal in the way! So, as soon as you stop, you'll topple over and hit the ground. It makes me flinch with claustrophobia every time I see them. In each incarnation of Knight Rider, I think part of the appeal is to say "Wow, that's a really cool car, I want one!" In this case, though, it had completely the opposite effect.
In the original series, KITT was based inside a lorry. In TKR, they used a huge aeroplane which could hold all 5 vehicles and had space for each person's living quarters. That's fair enough (although it must have been expensive to fuel!) but they also introduced some other bizarre ideas. For instance, one of the characters ("Trek") was a sci-fi fan; each vehicle was programmed to complement its driver, so Plato shared his interest. In at least one episode they got into trouble because Trek had taken Plato off to watch TV and the vehicles weren't allowed to leave the main storage area. In the original series, KITT was limited to part of the lorry, but that was just because there wasn't enough physical space for him to go anywhere else. However, he was always treated as an equal to Michael, and it seems wrong to treat the new vehicles as second-class citizens.
Overall, I don't recommend this.
Knight Rider (2008-2009)
This was much closer to the original series than TKR, although it still had enough differences to set it apart. For instance, none of the TKR vehicles had the red light on the front. By contrast, the new KITT (Knight Industries Three Thousand) has a split red light, which you can see in the intro:
Similarly, you can recognise the original music but the new tune is a tribute more than a remix.
When KITT used his Super Pursuit Mode there were outward mechanical changes. In the new series, it's all done with nanites: these allow for "attack mode", as well as transforming him into a 4x4 off-road vehicle. (Each variant vehicle is coincidentally made by Ford.)
The series started out with a TV movie as a pilot, but they made a few changes before the first proper episode so you don't need to watch it to know what's going on.
This does have some things in common with TKR. For instance, one of the drivers in TKR (Jenny) turned out to be Michael Knight's daughter. In the new KR series, Mike Traceur turns out to be Michael Knight's son. Neither of them was aware of this, but I suppose it makes sense, considering how he got around in the original series. Mike later changes his surname (like his father did), so there's a new Michael Knight driving a new KITT.
There's some dialogue in the first episode that I particularly liked:
Mike: "Ixnay on the surveillance footage-ay."
KITT: "Michael, why are you speaking Pig Latin? Incorrectly?"
It's quite common to see AIs with no grasp of idioms, e.g. in Star Trek TNG when Data doesn't understand the phrase "burning the midnight oil". This sets KITT apart, since he understood what Mike was trying to do and was snarky enough to point out that he was doing it wrong. This theme persists throughout the series, as KITT gradually becomes more autonomous.
As a related issue, the writers have put some thought into the implications of KITT's technology. For instance, the windscreen acts as a head-up display, so that Mike can have video chats with the people back at base. It would normally be dangerous for him to do this while he's driving, but KITT acts as a chauffeur leaving Mike's attention free to deal with other things. Similarly, the original KITT had loads of buttons (on the dashboard and the ceiling) which Michael had to keep pressing. The new KITT has a much simpler interface, since Mike can just tell him what to do.
Most of the episodes stand alone: it's best to watch them in order, but it won't matter too much if you don't. Initially, the team were involved with other government agencies, so they'd spend the first few minutes of each episode explaining the premise, e.g. a spy who'd stolen top secret information. I just tended to tune that out and hear "blah blah blah" until they got to the point: "you need to catch this guy and bring him back". Towards the end of the series there was a change of pace, and they focussed much more on small stories (e.g. an arsonist threatening a family-run bar), in common with the original series or The A-Team. I've often heard writers/fans complaining when "the suits" interfere with a series, i.e. executives come in and make changes to the writers' original vision. However, I think that this was a situation where they drastically improved the series by intervening.
On the whole, it's pretty good. It's not particularly deep or realistic, and it's not something I'd want to rewatch, but if I was a teenager then I'd probably love it and have nostalgia for it later. As an adult, it's fun, and I'd be happy to watch more episodes if they existed.