In English we just have one word for the conjunction "and" but in Japanese I so far only use "と" (to) but I know there is also at least "や" (ya) and "そして" (soshite) and the "-くて" (-kute) ending.

From comments to this question I'm also learning there are "~たり" (-tari) and possibly "も" (mo) which I naively think of as only meaning "too/also".

Are there any others and under which circumstances are each used. I know they are not even vaguely synonyms in Japanese but completely different from each other.