Just looking through the physical games. I probably have so many digital games with few owners since a lot of people don't care to track their digital collection here. Some of my JP Pokemon carts would qualify too, but I won't count those either since I know a lot of people own these carts, just not the specific imprints I own.
Oddworld Stranger's Wrath Collector's Edition (LRG PS3) - 14
Oddworld Abe's Oddysee Collector's Edition (LRG PS3) - 11
Jak X Combat Racing (standing cover LRG PS4) - 9
Jak & Daxter The Precursor Legacy (silhouettes cover LRG PS4) - 7
Ape Escape 2 (JP PS2) - 7
Ape Escape 3 (JP PS2) - 5
Jak 3 (facing away cover LRG PS4) - 3
Ape Escape Pumped & Primed (JP PS2) - 3
Pac-Man World Re-Pac (PS4) - 1... just me!
Animal Crossing City Folk with Wii Speak Bundle (JP Wii) - 1. Just me again
Mostly what I expected, LRG and JP games taking the lead. For regular NA games I think my "rarest" would have to be Duel Masters (PS2) with only 22 owners.