Investing in oil over the past decade has been like throwing a dart at a dartboard while intoxicated. You’re bound to score at some point, but the results can be pretty erratic. Oil is a highly demanded, finite commodity that has the ability to cripple growth when it trades above $100. But it also has the power to help generate growth, a point which investors often overlook.

Often disliked for the negative effects oil has on the environment, major oil and gas companies are responsible for employing tens of thousands of employees directly and creating countless downstream jobs once the oil leaves their refineries. ExxonMobil (NYSE: XOM), the poster child for the oil and gas sector and the largest company in the world by market value, employs more than 83,000 people and generated $383 billion in revenue just last year.

With so much cash flowing into the oil and gas industry, it’s not surprising to find some of the most stable and high-yielding dividends in existence parked in this sector. Let’s take a closer look at two major oil and gas companies that could provide stable but growing dividend income to your portfolio, while also highlighting one high yielder that you may want to pass on.

Chevron (NYSE: CVX) -- trust it
Rather than go with the largest company in the world, I decided on Chevron and its “paltry” $199 billion in revenue last year. Relative to ExxonMobil, Chevron boasts a faster near-term and long-term growth rate, as well as a lower forward earnings multiple, a higher dividend yield, and a stronger net cash position.

Pardon the pun, but what has been fueling Chevron’s growth is higher crude oil and natural gas price realizations. Beyond the 46% jump in the average selling price of oil from the year-ago period, Chevron also repurchased $1 billion worth of its stock during the quarter. Important to Chevron’s long-term success is its ability to regain permits to drill in the Gulf of Mexico, as well as increase its acreage owned in the valuable Marcellus shale region of the Eastern U.S. During the most recent quarter, Chevron made progress on both fronts. With natural gas expected to play an increasingly important role in energy generation in the coming decades, Chevron’s Marcellus acreage could prove invaluable.

Currently trading at only seven times forward earnings and yielding north of 3%, Chevron is already tipping the scales as a potential value play. Even more impressive, the company has grown its dividend at 9% annually since 2001. With a payout ratio of 26%, it seems very likely that this dividend aristocrat will be rewarding investors for years to come.

ConocoPhillips (NYSE: COP) -- trust it
This isn’t the first time I’ve highlighted Conoco in the oil and gas sector, and I can almost guarantee you it won’t be the last. I was torn between Conoco and BP (NYSE: BP), with its 4.6% dividend yield for the final spot among trusted dividend companies in the sector, but Conoco’s plan to split its oil and exploration business from its refining business next year was the driving factor in my selection.

The company announced in July that it plans to increase shareholder value by splitting its highly volatile refining segment from the dividend-seekers paradise section of its business -- the oil and gas exploration segment. In its latest quarterly filing, the company announced that its primary goal for the exploration segment will be moderate output growth and high-yield dividends. With a payout ratio of 30% and a current yield of 4%, Conoco has grown its dividend by an average rate of 13.9% over the past 10 years. As a current dividend champion, it appears very likely that the company’s dividend will be heading higher in the not-so-distant future.

Eni (NYSE: E) -- avoid it
I’m not purposely trying to pick on Europe, but a basket of macroeconomic and political problems could derail Eni for longer than just the next few quarters.

As the largest oil producer in Italy, Eni has been struggling with political problems in Libya for most of the year. Prior to the power struggle between Muammar Gaddafi and rebel forces, Eni was averaging 280,000 barrels of oil production per day. In addition, 12% of all natural gas used in Italy comes from Libya. Even with the political crisis shifting in favor of rebel forces and the end in sight, it will take upward of 18 months before Eni’s operations are fully back online.

Even more concerning are the macroeconomic worries swirling around Europe regarding the sovereign debt crisis. In what could be a self-fulfilling prophecy, wide-stretching austerity packages enacted by several European countries (including Italy) could push the region into a deep recession. While oil will always remain in demand, companies already weakened by external factors, like Eni, could be in line for a significant drop-off in earnings and revenue. My advice would be not to let Eni’s 5.6% dividend cloud your better judgment and instead to heed the company’s warning that production is going to fall short of previous estimates.

Foolish roundup
Once again we’re shown that the highest yield is not always the highest-quality yield. Dividend growth and a solid long-term outlook are the keys to successful dividend hunting. Chevron and Conoco both offer sustainable long-term growth and have put shareholders first for decades. Eni, on the other hand, appears just to be going along for the ride as Europe sinks deeper into the abyss.

What’s your favorite oil and gas stock for the long term? Share your thoughts in the comments section below and consider adding Chevron, ConocoPhillips, and Eni to your watchlist.