In my view there are two types:
1) When a game is only available on one platform.
2) When a game's best version (or a specific version) is only available on one platform.
For number 2, I consider Crysis and to a lesser degree, Cyberpunk, to be PC exclusives. I know that they are available on other platforms, but anyone and everyone will tell you not to play those versions.
In regards to a specific version, there are some Wii games that were supposed to just be ports of PS360 games which ended up being something else entirely, sometimes with re-written stories and entirely different levels. I consider those specific games as Wii Exclusives.
One known example is Sonic Unleashed. Some will claim the Wii version is better because there are less werehog levels and no explorable hub worlds, which in turn makes for a more streamlined experience.
Another example, Far Cry 1. For the longest time there was a console edition (with a different subtitle name) and a PC edition, with the console version having entirely different levels but the same story told differently. Eventually, the PC version was ported to consoles (with some small caveats), but essentially when playing Far Cry 1, people would recommend the PC version 9 times out of 10.
Thankfully today, 99% of the time devs have figured out console controllers and how to port to consoles better, so that odd waste of money and resources is behind us.