Apple's ambitious leap into streaming video illustrates an escalating trend: Tech's biggest companies, faced with limits to their growth, are encroaching on each other's turf.

Apple is taking on Netflix by launching a subscription TV service with its own original shows. Facebook is edging into Amazon's e-commerce sphere by enabling users to make purchases within Instagram. Google, which has already challenged Amazon and Microsoft in cloud computing, is launching an online game service that could undercut the lucrative game-console business at Microsoft and Sony.

Apple, which is also launching...