Surprisingly, that can be a difficult question to answer. Your status will always end on the date specified on your I-94, unless you have a non-frivolous application for change or extension of status pending with USCIS. After the date on the I-94 expires, you are considered "unlawfully present". Your status also ends when you violate it, for instance by working if your status is tourist, or by working for a different employer (or not working at all) than who sponsored your H-1B. In that case, you will be considered "out of status" but still lawfully present.

Finally, your status ends when the purpose of your visit has been completed. For instance, it ends upon graduation if you are an F-1 student, with the end of the exchange program if you are a J-1, or with the end of your employment as an H-1 or L-2.