I recently compiled a list of the 20 greatest companies I know.

These companies have not only shown dominance in the past, but also promise dominance in the future, with business models that allow them to crush competitors and earn excellent profits.

Today, I want to look out to the end of the decade, and highlight the companies that have the best shot at nudging aside some of my favorites to make my list of "20 greatest companies" in 2020. If they can do this, they will also almost surely rank as some this decade's greatest stock performers.

Let's run down a list of four strong contenders, before I predict which one I consider most likely to achieve elite status.

Contender: Apple (Nasdaq: AAPL)
We'll start with the company omission that riled up a host of the readers of my list.

To their point, Apple has a strong story. Its ability to reinvent itself from a computer also-ran to the "it" purveyor of all things high-end hardware in a decade is simply amazing. You could make an impressive tech portfolio entirely from the companies feeding off Apple's wake, including Cirrus Logic, TriQuint, Skyworks, and Zagg.

But Apple doesn't make the current list because I was looking for companies that are high-probability bets to be thriving years and years into the future. It's quite possible that Apple will do so, but it's no sure thing. Remember, the company was the subject of many a "what-went-wrong business case study" just a decade ago; it competes in a massively evolving and converging space against primo competitors; and it relies heavily on the iconic leadership of Steve Jobs.

It may surprise you to learn that I am contemplating picking up shares of Apple at current prices, but that's still a lower hurdle than being a top-20 company.

Contender : BP (NYSE: BP)
Do I really think BP will make 2020's "greatest companies" list? I wouldn't bet on it. But I don't preclude it, either.

Why? Let's look back at the reputational rehabilitation of one of its competitors. Recall ExxonMobil's (NYSE: XOM) Valdez oil spill in 1989. You may argue that BP's Deepwater Horizon spill was worse, but Exxon was still a laughingstock at the time, making environmental watchlists rather than lists of "great" companies.

Yet a couple of decades later, it's one of my 20 greatest companies. A Goldman Sachs analyst took it one step further in 2008, saying, "It's the world's greatest company, period."

It's a high hurdle for BP to reach Exxon's heights, but at the very least, I'm looking at history and thinking about BP as a possible investment.

Contender: Annaly Capital (NYSE: NLY)
From its inception in the late 90's, mortgage REIT Annaly Capital has been a serious moneymaker for investors, returning more than 500% to shareholders, including dividends. I don't have to remind you how poorly the market as a whole has performed in that time.

Its dividend yield currently stands at 14.3%, and prospective investors wonder whether it can keep up these serious dividends (and overall returns). As I've detailed before, Annaly makes its money off of the interest rate spread between its borrowings and the agency-backed mortgage-related securities it buys.

Throughout most of its history, Annaly has enjoyed the one-two Greenspan-Bernanke punch of historically low interest rates on its borrowings. If we enter a harsh interest rate environment, Annaly's dividend won't stay at these elevated levels. But this cyclicality doesn't preclude market-beating returns. If we see Annaly come through tougher times with strong returns, it may be hard to deny Annaly and its CEO Michael Farrell a spot on the list in 2020. Of course, that brings up the Steve Jobs-like problem of iconic leadership...

Contender: Intuitive Surgical (Nasdaq: ISRG)
Now this is a growth story. Intuitive Surgical grew earnings per share by 96% in 2007, by 38% in 2008, by 16% in 2009, and by 60% last year. Analysts expect 17% growth this year, and another 17% in 2012.

Intuitive is literally cutting-edge as it seeks to revolutionize surgery through robots. Unlike other futuristic-sounding companies, though, Intuitive Surgical isn't some pie-in-the-sky concept that only sounds good in theory. Its da Vinci surgical systems are already in use and wildly profitable, and Intuitive has net margins of 27%.

I own shares of Intuitive Surgical and it almost made the cut of my current list of 20 greatest companies. If it keeps on keeping on, it'll surely make 2020's list.

My No. 1 Contender
You may have guessed from my glowing write-up above, but I believe Intuitive Surgical has the strongest shot of making my list of the 20 greatest companies in 2020. It rides the megatrend of finding cheaper, more effective health care as we face increasing constraints. And it pursues its goals off an already impressive base of profits. We shall see.

If you'd like one more great company to consider, click here for our free report: The Only Energy Stock You'll Ever Need. Hint: It's not ExxonMobil or BP.

Anand Chokkavelu owns shares of Intuitive Surgical and ExxonMobil. A person with the ticker symbol TRU heads his list of 20 Greatest People of 2011. Apple is a Motley Fool Stock Advisor pick. The Fool has written puts on Apple. Motley Fool Options has recommended a bull call spread position on Apple. The Fool owns shares of Annaly Capital Management, Apple, ExxonMobil, Cirrus Logic, and TriQuint Semiconductor. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.