Exxon Mobilhas scrapped with Venezuela's Hugo Chavez over nationalized oil projects and sparred with U.S. senators over high oil prices.
But the toughest challenge that Exxon , the world's largest oil company, may be facing in recent years comes from its own ranks: A group of dissident shareholders pushing a proposal to split Exxon's chairman and chief executive positions at Wednesday's annual meeting.
Rex Tillerson currently holds both jobs.
The company recorded two of the largest-ever corporate profits in history in 2006 and 2007, but a growing group of shareholders has publicly backed the proposal, citing Exxon's lack of investments in alternative energy as their main motive.
The Rockefeller family is leading the charge, calling for a change at the top of the company that is closely tied to their famous fortune.
John D. Rockefeller founded the Standard Oil Co, Exxon's precursor, in 1870, but the family has not been actively involved at Exxon for years. The company said no Rockefeller has served on its board, or the board of any of its predecessor companies, since 1911.
Peter O'Neill, great-great-grandson of Rockefeller, said 66 of the 78 adult Rockefellers currently supported their stance.
It is unclear how many shares the Rockefeller family controls. Exxon was able to identify 12 of the 15 Rockefellers associated with the shareholder resolution, and said they collectively own around 332,000 of the company's 5.4 billion shares -- or about 0.006 percent of outstanding shares.
The family has been moved to act, driven by Exxon's passivity in what they see as an important emerging market.
Neva Rockefeller Goodwin, a great granddaughter of John D. Rockefeller and a Tufts University economist, called on Exxon to reconnect with the forward-looking vision of her ancestor.
"Part of John D. Rockefeller's genius was in recognizing early the need and opportunity for a transition to a better, cheaper and cleaner fuel," Goodwin said in April.
Exxon has urged shareholders not to support the proposal to split the top jobs, saying it believes the most effective leadership structure for the current company is for Tillerson to continue in both roles.
Tillerson took the helm of the company at the beginning of 2006 and has steered a course similar to that set by his predecessor, the often combative Lee Raymond.
In Tillerson's time as CEO, Exxon has raised its spending on oil and gas projects, but has not made any significant moves into renewable or alternative energy.
Dissidents have also criticized the company for having a monolithic corporate culture, which prevents it from moving in new and innovative directions.
Exxon also faces 16 other shareholder proposals at the annual meeting, all of which the company suggested shareholders vote against.
They include seven proposals about the company's environmental policies and impact and three proposals on Exxon's executive compensation.
Another proposal asks shareholders to vote to prohibit nonbinding or advisory shareholder proposals, unless the board takes specific action to approve such proposals.
Exxon's rival Chevronwill also hold its annual meeting on Wednesday in San Ramon, California.