Dividend stocks should be the core of any investor's portfolio, but oversize dividends could be a red flag for investors. It can be a sign that the market is expecting real trouble for the company, and if a big dividend is cut by management, an attractive dividend yield can disappear overnight.

Take EarthLink (Nasdaq: ELNK) as an example. As recently as the beginning of 2011, the stock had an impressive-looking trailing dividend yield of around 7.3%. But the dividend was so high because the business was slowly deteriorating and management was giving as much back to investors as it could. Today, the stock is down over 20% from that point, and the dividend yield is only 3%.

We should look at oversize dividends with caution, but sometimes high yields don't come with a "Do Not Touch" sign. Here are three stocks with both high yields and strong futures.

Grocery stores and milk
I will admit, I may be a little biased here. Full disclosure: I go through an unusually large quantity of Roundy's (NYSE: RNDY) milk, so you can read this with the appropriately sized grain of salt.

Roundy's hasn't been a public company long, completing its IPO in February of this year, and it's been a bit choppy for the company already. The IPO priced under its anticipated range, and worse-than-expected second-quarter numbers sunk the stock. But that doesn't mean that the grocery business is suddenly in danger of collapsing.

On the plus side, Roundy's sales grew 1.7% in the second quarter. The flip side is that a 3.2% decline in the number of transactions led to a similar decline in same-store sales. The decline was largely due to the floundering economy, and I don't see it as a sign that the business will disappear. Whole Foods may be taking share at the present moment, but with Roundy's trading at just 6.8 times the bottom end of this year's adjusted earnings estimates and with investors getting a whopping 12.3% dividend yield, I think Roundy's is still a decent buy.

The energy dividend play
Energy and food are two of only a few things that we'll definitely need long into the future. One of the ways oil explorers are adding production these days is in ultra-deepwater, drilling up to two miles under the surface of the ocean.

Seadrill (NYSE: SDRL), with its 8.2% dividend yield, is a play on this energy source, not by investing in the wells themselves but by owning the rigs doing the drilling. In the second quarter, Seadrill's revenue rose 7%, and operating profit grew 6% -- and the company shows no sign of stopping. Three of the company's rigs are booked beyond 2016, and dayrates have risen to near records of around $600,000 per day.

Seadrill's advantage over competitors like Transocean (NYSE: RIG) and Noble is that it is more leveraged to the ultra-deepwater market. With the industry undersupplied and demand looking to remain strong for years to come, this should be a safe dividend and could even provide some nice price appreciation.

Growing what we eat
Fertilizer isn't the sexiest business in the world, but it is extremely profitable. With the population growing and farmers needing to get everything they can out of an acre of land, fertilizer is a valuable piece of the puzzle. Terra Nitrogen (NYSE: TNH) provides the base ingredients for that fertilizer, and its strong business has led to a major cash flow opportunity for investors.

Demand and prices will swing up and down quarter to quarter, but the overarching trend here is that we need more food from less land, and Terra Nitrogen is a play on this.

But there is a catch with this dividend play. Terra Nitrogen is an MLP, which can make taxes complicated, so the extra work isn't for everybody. The plus side is, Terra Nitrogen's dividend yield stands at 7.9%, a high yield even for an MLP.

Foolish bottom line
I think Roundy's, Seadrill, and Terra Nitrogen present not only high dividends for investors, but also relatively stable businesses long-term. High-dividend stocks need to be watched closely by investors to look for signs of a seriously deteriorating business, but I like where they're at right now.

For more on one of my favorite energy stocks, Seadrill, check out our premium report on the stock. It gives background on the company and highlights the three areas investors must watch. It also comes with a year of updates on the company, so find out more by clicking here.