In residential plumbing systems, some of the most common fittings include elbows, tees, couplings, adapters, reducers, nipples, and valves. Elbows are used to change the direction of pipes, while tees create branching connections. Couplings and adapters allow for simple pipe connections, and reducers are used to transition between different pipe sizes. Nipples serve as short extensions or connectors, and valves provide control over fluid flow.