Most of the things I own are PAL games so probably not worth the match, never mind the fuel, used to burn them were I getting rid of them.
Likewise I don't actually know the "rarest", by which I mean most expensive, games for a given system as you in turn get things like NCAA College Basketball 2K3 on the gamecube (it is a sports game, aka the dross you usually have to filter through in car boot sales and charity shops, but apparently it is really rare and so expensive as a result) the wind waker/metroid double pack on the gamecube -- while the base games don't go for lunch money this disc apparently clocks hundreds (it only came bundled with systems for a limited period or something).
By and large I have not really sold or traded anything from the PS1 on up. To that end as nobody wanted them at the time I have a reasonable collection of most of the good PAL N64 and GC games, even still have the cardboard boxes for most of the N64 games (albeit flattened and stuck in another cardboard box). PS1 I did not accrue quite as nice a collection for but it seems some of the final fantasy games and similar don't go for nothing.
I did once pay up for a boxed copy of Tetris Advance, aka the one good commercial tetris on the GBA
http://www.success-corp.co.jp/software/gba/tetris/ but I see I can now find that for a 1000 yen.
I mostly only collect games I like or that have a really nice example, or early example, of a given mechanic or gameplay style, or maybe something notable in the censorship world. Kind of kicking myself for not picking up a stack of sega CD games at the dump a while back as it would have meant I own a copy of night trap.