Tracking down a stock that pays a high yield is easy enough to find, but selecting ones that are worth holding onto for decades to come is quite another thing. Not all high-yield stocks are stable enough, or have enough cash coming in to keep payouts flowing.

That's why we reached out to a few Motley Fool contributors to find three high-yield stocks that dividend investors can buy -- and comfortably hold -- for years to come. They came back with ExxonMobil (NYSE:XOM), American Tower (NYSE:AMT), and AT&T (NYSE:T). Here's why.

Piece of paper that says "dividends" sitting on top of $100 bills.

Image source: Getty Images.

Big oil, big opportunity

Todd Campbell (ExxonMobil): It's true that ExxonMobil shares have been underperforming its peer group in the past year, but in my view, that underperformance is presenting an excellent opportunity for income investors to add this big oil stock to their forever portfolio.

ExxonMobil's lackluster share price returns are in part due to concern over decelerating production, including a 2% dip in 2017. Declining production isn't helping the top line, but there's reason to think that once a few of ExxonMobil's key projects begin pumping out oil, they'll be able to more than offset the declines associated with maturing oil.

The project offshore of Guyana, for instance, is a massive one that could generate 500,000 barrels of oil per day, including 120,000 barrels per day as early as 2020. Guyana's even more attractive because a low $26 per barrel breakeven point means that if oil prices remain anywhere near where they are today, it will be a boon to ExxonMobil's bottom line.

Other projects, including U.S. shale and offshore Brazil, also offer significant opportunity. Exxon's Permian Basin and Bakken shale production grew 18% year over year in Q1, and the company has over 2 million net acres offshore of Brazil that could help move the needle in a few years.

It also shouldn't be ignored that ExxonMobil's financial results are down from five years ago because of lower oil prices, but oil prices have been climbing this past year, and as a result, the company has an opportunity to leverage the cost-cutting it did during oil's downturn for higher earnings in the future.

Overall, higher oil prices, the potential for production to grow over time, and a juicy 4.4% dividend yield make ExxonMobil one of my favorite set-it-and-forget-it stocks.

Rock-solid business equals fantastic dividends

Anders Bylund (American Tower): When I'm looking for an industry with decades and decades of staying power, wireless networks easily spring to mind. Not the network providers themselves, of course, since that industry is intensely competitive, and it's difficult to pick out any long-term winners there. No, I'm talking about the infrastructure behind it all.

Say hello to American Tower, a global leader in the business of making wireless networks tick.

The company owns and leases more than 40,000 network sites in the U.S. alone, and that's just 25% of American Tower's worldwide footprint. Other hotspots of infrastructure investments include India, Brazil, and Mexico. American Tower pursues both the international and domestic markets mostly through acquisition.

The four big American networks have largely handed off their tower and small cell site management to American Tower and a handful of rivals, leasing back the tower properties they once constructed and owned. Similar deal structures are becoming popular all around the world, allowing the networks to focus on running their mobile data and voice services while American Tower and friends double down on the property management and infrastructure maintenance that they do best.

Being structured as a low-tax real-estate investment trust (REIT), American Tower must send out at least 90% of its taxable income in the form of dividend payments. That's the shareholder-friendly catch that lets REITs qualify for extremely low corporate tax rates. So American Tower funnels essentially all of its pre-tax income straight into its dividend program, resulting in juicy payouts and generous yields.

All told, American Tower has raised its dividend payouts every year without fail, going back to the original policy in 2011. The dividend checks have more than tripled in size over the last six years, and annual yields are hovering around 2%.

And I dare say that this dividend will stick around for the very long haul, only growing larger and more wealth-building over time. That's why I own some American Tower myself and would recommend this stock to any hunter of long-term dividends.

A strong telecom with a history of dividend stability

Chris Neiger (AT&T): AT&T has gone through a bit of a rough patch lately -- its shares are down 15% compared the S&P 500's 15% gains over the past year -- but that's no reason for investors to give up on this telecom dividend play just yet.

For starters, income investors will be delighted to know that the company pays a very generous 6% yield and has a 34-year track record of raising its dividend. If that's not enticing enough, consider that AT&T has a massive opportunity in the burgeoning 5G wireless market and could dominate the content market if/when its deal to buy Time Warner goes through.

AT&T is fighting the Department of Justice to get the acquisition approved, and while it's still up in the air, AT&T CEO Randall Stephenson said on the company's first-quarter call that AT&T is optimistic the deal will go through. Stephenson mentioned at an investor conference this month that the acquisition will bring a "sizable monetary opportunity" by combining its advertising efforts between wireless, cable, and Internet customers.

AT&T also holds a huge opportunity in the growing 5G wireless market. This new technology will allow for more wireless connections, faster speeds, and lower latency (i.e it can send lots of information very quickly), all of which means that wireless customers will soon have even more reasons to use lots of data and spend more time on the company's vast network. The telecom is already conducting 5G tests this year, and a commercial rollout is expected in some major cities as early as next year.

While AT&T waits out the legal decision for its Time Warner acquisition, there could be some more volatility with the company's stock. But long-term dividend investors should look at AT&T's long history of consistent and rising dividend payments and know that this company is likely to keep its dividend investors happy for many more years to come.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.