Most of the time if you are catching another plane from the same airline that is going to a destination in another country you can do so without going through immigration. If you must go through immigration to get to the new flight they will absolutely check your passport.

Whether you need a passport for a connecting flight depends on the nature of your journey and the airport's layout. For domestic-to-domestic connections (e.g., Chicago to New York), you only need a government-issued photo ID. For international-to-international connections at major hubs like Dubai or Singapore, you generally stay "airside" in the international transit area and do not need to clear immigration, though you must still have your passport to board the next flight. However, if your connection requires you to change terminals that are not linked airside, or if you are connecting in the United States or Canada, you are often required to clear Customs and Immigration even if you are just passing through, which necessitates a valid passport and potentially a transit visa. Always check if your connection is "through-checked"; if you have to reclaim and re-check bags, you will definitely need your passport to exit and re-enter the secure zone.