Apple Inc. (NASDAQ: AAPL) has been on a decade-long roll that is the envy of most corporate executives.  Since 2003, Apple's revenue has grown at a 38.1% average annual rate, swelling to $158.5 billion from $6.2 billion. EPS has ballooned to $44.15 from $0.10 over the same period – a remarkable 83.8% average annual growth rate.  At the same time, Apple's average share price has gone from $9.45 to $557. This remarkable share-price appreciation has lifted Apple's market cap to $515 billion from $6.9 billion (based on average prices and average shares outstanding).  Apple is, quite simply, the world's most valued company .  The iPhone, the iPad, the iPod, the Mac … Apple hasn't missed in many years, and its products continue to resonate with consumers today. Apple's unrelenting success has led many to tinker with the thought that it could be the first company to demand a trillion-dollar market cap.  There is no denying Apple's success. Still, I wouldn't bet on it becoming the first trillion-dollar company.  The same trillion-dollar chatter reverberated around Cisco System (NASDAQ: CSCO) and Microsoft (NASDAQ: MSFT) in late 1999, when the former's market cap was above $500 billion and the latter's broached $600 billion. Both Cisco's and Microsoft's market caps are far below those lofty peaks today - $105 billion and $230 billion, respectively.  History is replete with examples of hot technology stocks faltering. Competition in the sector is fierce, and consumer fatigue is a mitigating factor. The mini iPad and iPhone 5 are terrific products, to be sure. But even they lack the “oomph” of previous Apple releases.  So if not Apple, then who would I pick to be the first to reach a trillion dollars?  I would go with ExxonMobil (NYSE: XOM) , whose $411 billion market cap is second behind Apple. Yes, ExxonMobil indeed trails Apple by $100 billion, but this is a tortoise-and-hare race. Hares, which are often represented by technology, tend to peter out. Tortoises, like integrated energy, continually plow forward.  ExxonMobil is the number-one tortoise in integrated energy. It rarely regresses, and when it does it quickly calibrates and continues moving forward. From 2002 through 2011, ExxonMobil's revenue grew at an 8.2% average annual rate, EPS grew 18%, and market cap grew 5%.  These growth rates aren't terribly impressive when juxtaposed to Apple's. Keep in mind, though, ExxonMobil generates $486 billion in annual revenue, which is three times Apple's annual revenue. ExxonMobil is a huge enterprise.  Dividends will also help keep the needle moving forward. ExxonMobil might well be the ultimate dividend-growth company. Its dividend history dates back to the days of the Standard Oil Trust.  Over the past 30 years, ExxonMobil's dividend has grown at a 6% average annual rate. Over the past 10 years, the average annual rate of growth has risen to 7.2%.  What's more impressive is the ease at which ExxonMobil can pay and grow its dividend. In 2011, it paid $8.5 billion in dividends. That's a big number, but it was only 22% of its net income and only 36% of its free cash flow.  As dividend growth goes, so goes share price growth. Persistent dividend growth is a primary factor in ExxonMobil's share price nearly tripling over the past decade. That said, the number-one reason I favor ExxonMobil over Apple is that I know that 25 years from now the demand for oil will continue to be robust. In contrast, I don't know if the demand for iPhones or iPads will remain robust even five years from now.  At the turn of the millennium, a Nokia (NYSE: NOK) phone was the must-have mobile device. Over the past five years, Nokia has been relegated to also-ran status by Google (NASDAQ: GOOG) and Apple smart phones.  One doesn't have to think too deeply to imagine Apple suffering a similar fate to Nokia, or, perhaps more likely, to Microsoft. Microsoft is still a good company, but many of its products and services have been supplanted in the consumer market by hipper, more progressive offerings.  One also doesn't have to think too deeply to imagine another publicly traded integrated-energy company supplanting ExxonMobil, because there simply isn't one. ExxonMobil has been the big dog in integrated energy for decades. I don't see that changing.  That's why I'm placing my bet on ExxonMobil to be the first member of the trillion-dollar market-cap club.