Start with the obvious three
Check the breaker, because a tripped breaker can look almost closed. Press RESET on every GFCI in the kitchen, bath, garage, basement and exterior. Then check whether the outlet is switched, since half-hot receptacles controlled by a wall switch are common in older living rooms.
The hidden culprit: back-stabbed connections
Builders often push wires into the spring clips on the back of a receptacle instead of using the screw terminals. Decades of heat cycling loosen that clip, and because the outlet also feeds downstream devices, one failure kills several outlets at once. The fix is re-terminating on the screws.
Open neutrals and why lights get strange
If lights brighten in one room while dimming in another, or voltage reads high on some circuits and low on others, suspect an open or shared neutral, possibly at the service. That is an urgent call, not a DIY project, because it can destroy electronics and appliances.
Stop and call immediately if...
You see scorching, melted plastic or a browned outlet face, you smell burning, the cover plate is warm, or plugs fall out loosely and arc. Turn off the breaker and call a 24 hour electrician.