Hi Alan,
Interesting issue you raised re. Cats interbreeding, but Apes/monkeys not...
Regarding Cats:
Yes, Lions & Tigers can breed (both has 38 chromosomes), but this hybrid will usually be sterile. At meiosis, when sperm/egg cells are created, the chromosomes need to lign up to allow homologue pairing & cross-over to occur. If the chromosomes are not the same size, this can not occur, when the cell then does divide to form haploid cells (and it is likely not to), it don't end up with a copy of each chromosome it needs, and/or multiple copies of some, and none of others. either Over and above all these obstacles, issues like growth dysplasia also will come into play. Not sure if 2 Litigers ever had a successful mating,but even then you might still have the same issue around chromosomes lining up. My assumption would be that the cats are more closely related (i.e. evolutionary speaking) than apes & monkeys.
Alan,
You might find the following website pretty interesting !
http://www.hemmy.net/2006/06/19/top-10-hybrid-animals/