I have problems with 'the animal flavor of the day' (challenge animals), popular animals and, strange as it may seem, okapis. Yes, okapis. Thanks to the trading center being way too small to set up multiple breeding programs I had to trade my male okapi offspring to make room. Unfortunately, when my male breeder okapi died there weren't any male okapis on the trade center. At all. Only five or so females. I only managed to get a male okapi today (after more than a day of waiting) and it's of abysmal quality compared to the gold quality okapis I managed to breed. So now I'm 'forced' to always keep a male AND a female okapi in my trading center as well to make sure I don't 'lose' good breeding quality okapis.
Also, buffalos. Female buffalos. They're rarer than male okapis, rhinos and giant pandas combined.