Investors want just one thing from the world’s biggest oil companies: cold, hard cash. But it is becoming harder for the oil giants to deliver.

Companies such as Exxon Mobil Corp., Royal Dutch Shell PLC and BP PLC have long used hefty and reliable dividends to keep investors on board in a sector that has volatile profits tied to commodity prices. The importance of the payments has only grown recently, as investors have become wary of the companies due to short-term concerns about oil overabundance, and long-term fears that...