Lions and tigers used to coexist over a very wide area, but there is no record of them ever breeding together in the wild.
In zoos, that's a pretty common occurrence. The offspring are called tigons, or else ligers, depending on which species was the mother. It seems to have something to do with boredom.
There are many other examples. For instance, siamangs can breed with common gibbons, and the domestic horse with Przewalski's wild horse , , , . (This last is in spite of a mismatch in the number of chromosomes: Przewalski's has 66, domestic horses have 64.)