Good thread.
Some people have mentioned some games that I don't think are rare, or at least I'm not aware of it. Perhaps they're just younger gamers who have had to go out of their way to find games from previous consoles that older gamers picked up as they came out. For example, someone said they have the non-platinum versions of Final Fantasy VII, VIII and IX on the PSX - I have those too, in fact my brother and most of my friends also have all of those, as we all just bought them as they came out, so I thought everyone had them. I've also got non-platinum versions of X, X-2 and XII as well as strategy guides for all of them, including the limited edition hardback guide for XII (which looks gorgeous with the dust jacket removed). Someone has even said Call of Duty 4 - are you kidding?! If that's the rarest game you own you must only buy games that are amongst the best selling games ever because that's sold 13 million copies! And someone said 'I doubt anybody's heard of Cossacks II The Napoleanic Wars'. Well, as an RTS fan since Dune 2, of course I've heard of it!
That said, I do have some games which I think are rare. Such as:
X-Beyond the Frontier, and X-Tension, its expansion pack (PC-CDROM)
Both bought upon their release, I was recently having a clearout and checked eBay to see what these would sell for. All I could find were copies of X-Gold. The last big box version of the original game had sold for £40.
Ghost in the Shell (PSX)
I once rented this from Blockbusters and didn't complete it. I went back to rent it again and they no longer had it. So I started searching for it and could only ever find £30+ copies of it on eBay. Fortunately my then-girlfriend worked in a video games store and set aside a copy one day when somebody traded it in.
Resident Evil - Director's Cut (PSX)
Not sure how rare this is, but I had a really hard time tracking down a copy of this. Ultimately a friend found me a copy for my birthday.
And I have lots of other games for older platforms that might be rare. Lots of big box PC games from around 10 years ago and lots of Amiga games that are at least 15 years old. I used to have a Commodore 16 and a game I had for that was called 'Cuthbert Enters the Tombs of Doom II'. I've never heard anyone else mention that game ever, nor have I ever managed to find a copy of the first game...