We use indefinite articles for non-specific singular nouns; for example, "a banana."
Is that a banana?
I would like a banana for breakfast this morning.
I like banana is not correct if you are referring to the non-specific singular noun. If you were given a number of choices for, let's say colors, you could use such a phrase. For example, "which of the colors do you prefer: orange, peach or banana? I like banana."
I like bananas is a statement of fact that you like bananas (plural) in general.