My favorite example, in Chinese-speaking families, is just how common it was for people to say "open"/"close" the lights, instead of turning on/off the lights.
Also, in Chinese, "no" is not a complete sentence in answering a yes/no question, so the way one generally says no is to just repeat the verb in the negative: "Are you going to the store?" is answered with "Not going." So sometimes native Chinese speakers repeat the verb when speaking in English, too.
And my personal favorite example, is how the phrase "long time no see" entered the English lexicon: the two leading theories are that it either came from Native American or Chinese speakers. I wouldn't take sides on that debate, but will note that it pretty directly fits a direct translation of the Chinese phrase.