What do I use? That depends on the tanning method of the leather, the finish, what the article is, use etc.
General Examples:
Oiltanned Leather (harness boots, some heavy leather coats): Huberd's Boot Grease
Chrometanned leather (garments, uphoulstery etc): Aussie Leather Conditioner, Huberd's, Pecard's
VegTan: Aussie, Huberds or Pecards
Exotics: Pecard's Exotic Leather Dressing
I prefer non-animal based products, not for the stereotypical reasons (I am a carnivore..we hunt....vegetarian is an ancient native american word meaning 'bad hunter') but because animal fats are not as stable as other products, tend to go rancid quicker and are a good medium for bacteria growth. The only animal based product I personally use for some leathers is a dubbins but the fats are rendered in dubbins which makes them more stable and less likely to be a medium for bacteria. Bee's do not qualify as animals in this case as beeswax is very stable.
It's difficut to suggest a particular conditioning product without knowing what it is being used on.