The usual reasons for rebuilding an engine are loss of compression, excessive oil consumption, or excessive oil clearances. The symptoms of loss of compression are extended cranking (hard to start), lack of power, or a misfire (running rough).
Is it worth it to rebuild an engine?
A rebuilt engine gets better gas mileage than your old one and will emit fewer pollutants. Rebuilding engines also saves energy related to processing discarded engines and cars. A remanufactured/rebuilt engine, with proper maintenance, is capable of lasting as long as a new car engine.
Is it cheaper to rebuild an engine or replace it?
A scheduled overhaul is almost always less expensive than a new engine. Rebuilding to repair is usually cheaper than buying a new engine, too. You may save up to half of the cost of a new engine by rebuilding. However, sometimes rebuilding is not a good option.