Nikon has done a remarkable job in maintaining backwards compatibility with their camera lenses. Back in the 50's when they developed their first SLR camera, they designed the Nikon F-mount, named so because their camera was called the Nikon F. It mounted to the camera with a quarter turn, and had a little metal tab on the side to hook up with the metering system.
As their cameras did well, they designed newer and better cameras - with newer and better metering systems. This included a partial redesign of the F-mount - the AI mount. This still had the metal tab for the older camera's metering system, but the new AI mount had ridges cut into the aperture ring which allowed the lens to interface with the metering system in a much less obtrusive manner. This was first done during the later Nikkormat and Nikon F2 days. Another feature was ADR, which stood for aperture direct readout. This was a system of tiny mirrors that allowed you to see what aperature you had set the lens to while still looking through the viewfinder. On the lens, this required tiny numbers on the the aperture ring at the right place. But even with the advent of the AI version, the F-mount was still reasonably backwards compatible. Older cameras could use the newer AI lenses with no modifications, and newer cameras could use the older lenses to a certain extent. Some of the newer cameras had a flippable tab on the aperture sensing ring, allowing you to mount the older lenses and use them - without automatic metering. Or, you could spend a reasonable sum of money (~$50 US) to have your older lenses modified to fit the newer AI metering system.
Yet another redesign occurred with the introduction of the Nikon 2000 (or Nikon F301 in other parts of the world besides the US). These had more advanced automated exposure modes. In order for the camera to set the shutter speed correctly for longer (~100 mm and longer) lenses, the AIs system was developed. This was simply a little scalloped out portion on the mounting ring which was sensed by a little metal nub on the camera. Again, Nikon did a great job on the compatibility front, making AI and AIS pretty much totally compatible except for the fact that with longer lenses, the newer cameras might not automatically pick the best shutter speed.
Now, during this period when most other camera manufacturers had made obsolete at least one of their lens mounts, Nikon managed to maintain compatibility for the most part. But during the advent of autofocus, even the die-hard Nikon fans assumed that they would have to change their camera mount. They were wrong!
The AF (autofocus) mounts are pretty much the same, except they have the contacts and connections required for autofocus. They did lose the original F-mount tab, however, so they cannot meter automatically with the oldest of the Nikon cameras. However, they work perfectly well with most AI and AIs compatible manual focus cameras. And the older lenses work on the new autofocus cameras, without autofocus, of course.
Even with the introduction of an APS Nikon camera (Nikon Pronea), they managed to keep compatibility, at least in the lens mount ring. Heck, they even kept the F-mount for their pro-level digital cameras (the Nikon D1 and its variants).
Overall, a stunning achievement in product design and commitment and respect to their customers.
There are a few exceptions, of course. The most obvious may be the failed Nikon F3AF and its lenses, which no one talks about anymore...
This means that if you are into getting used camera gear, the Nikon system is very, very hard to ignore, as you have roughly 50 years worth of manufacturing in a compatible system. Unfortunately, this also means that used Nikon gear is still expensive.
And I almost completely forgot. The compatibility also means that YOU CAN STILL BUY NEW LENSES FOR YOUR 35 YEAR OLD CAMERA! This kind of thing is pretty much unheard of in manufacturing. Sure, you can still get parts for your Nash Metropolitan, but is Nash still making the parts? No! (Nash doesn't even exist anymore, does it?)
And as mturner pointed out, and I forgot to include, is that you can buy 35 year old lenses and slap them onto your brand new Nikon D1x super-duper digital camera. Not that you'd want to, but around 15-20 years ago or so, there were some nice manual focus lenses, like the legendary Nikkor 58mm f1.2 Noct lens. Or maybe you spend all your money on the camera, and can't afford a nice lens (foolish!). You can shell out $25 and get a common Nikkor 50mm f1.8 lens and use that until the next paycheck.
This means you can shell out more for a high-end zoom lens for a camera you bought way back when, and end up paying more than you did for the house you bought when you bought the camera.