innumerable

Innumerable means too many to be counted. Not infinite — simply past the point of counting.

It goes before a plural noun, so innumerable occasions or innumerable small kindnesses, and it is a deliberate exaggeration. Countless does exactly the same job and is far commoner in speech, which leaves innumerable sounding formal and slightly literary. The word is built from numerable with in- in front, though numerable itself is almost never used on its own.