You won't have any trouble finding stocks with high dividend yields of 4% or more. There are hundreds of them. But many high-yield stocks are ones you shouldn't touch with a 10-foot pole. Their dividends are just too shaky. 

There are some solid dividend stocks that yield 4% or more that do appear to be great picks to buy right now, though. Here's why AbbVie (NYSE:ABBV), Brookfield Infrastructure Partners (NYSE:BIP), Medical Properties Trust (NYSE:MPW), and Verizon Communications (NYSE:VZ) especially stand out.

Five increasingly higher stacks of coins with blocks on top of each stack that spell out "Y-I-E-L-D"

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1. AbbVie

Big drugmaker AbbVie pays a dividend that yields nearly 5.5%. The company has boosted its dividend by an impressive 168% since Abbott Labs spun it off in 2013.

AbbVie's immunology drug Humira remains the world's top-selling drug. Humira now faces biosimilar competition in Europe, and biosimilars will enter the U.S. market in 2023. However, AbbVie isn't worried.

The biopharma company's current lineup includes a couple of cancer drugs with tremendous momentum -- Imbruvica and Venclexta. AbbVie's endometriosis drug Orilissa is likely to become a blockbuster success. The company also claims a strong pipeline that includes two of the most promising immunology candidates in years, risankizumab and upadacitinib.

2. Brookfield Infrastructure Partners

Brookfield Infrastructure Partners' dividend yield is 4.98%. The limited partnership's goal is to increase its dividend by at least 5% annually. Over the past five years, Brookfield Infrastructure has done even better, raising its dividend by 57%.

The company's business model should ensure the dividend checks keep flowing. As its name implies, Brookfield Infrastructure focuses on infrastructure assets. Its assets include communications towers, energy transmission lines, ports, railroads, and toll roads. These infrastructure assets provide the company with a steady revenue stream.

Demand for infrastructure will increase in the future, especially as the economies of developing countries expand. Brookfield Infrastructure CEO Sam Pollock noted in the company's Q4 conference call that he thinks there could be great opportunities in South America especially. Pollock said Brookfield Infrastructure plans to "buy higher-growth businesses, where we can apply our operational expertise, thus earning higher returns." That's what dividend investors like to hear. 

3. Medical Properties Trust

Medical Properties Trust's dividend yields 5.53%. Because it's organized as a real estate investment trust (REIT), MPT must distribute at least 90% of its taxable income to shareholders in the form of dividends.

The company owns 276 healthcare properties in the U.S. and several other countries. Last year, 76% of MPT's total revenue came from general acute care hospitals. MPT leases its facilities to healthcare operating companies through long-term leases that require the tenants to assume most of the costs associated with the properties. It also makes mortgage loans to some healthcare operators, with their real estate assets serving as collateral.

MPT stock has performed really well over the last year, reaching an all-time high in February. The company ranked as the No. 1 healthcare REIT over the last 10 years in total shareholder return. With its dependable revenue stream from leasing its current properties and opportunities to expand in more international markets, MPT appears likely to continue to generate solid returns for investors and keep the high-yield dividends coming.

4. Verizon

Verizon pays a dividend that currently yields 4.33%. Its dividend hasn't increased by a whole lot in recent years. However, the telecommunications giant has increased its dividend for 12 consecutive years.

Although Verizon competes against formidable rivals, it's still the No. 1 wireless provider in the United States. Verizon claims to have the best nationwide wireless network in the nation and continues to attract new subscribers while holding on to most of its existing customers.

One huge opportunity for Verizon that's just getting started is high-speed 5G networks. Verizon launched its 5G Home service in a handful of cities in October 2018. The company should enjoy solid growth as it rolls out its 5G services throughout the U.S. over the next few years.   

Some risks, but solid overall

Each of these dividend stocks faces some risks. AbbVie's pipeline candidates could stumble in clinical studies. Brookfield Infrastructure, Medical Properties Trust, and Verizon could be hurt if interest rates rise significantly. All of the stocks could fall if the global economy falters.

However, each of these companies claims a solid business model with viable long-term growth prospects. AbbVie, Brookfield Infrastructure Properties, Medical Properties Trust, and Verizon should appeal to investors seeking reliable high dividend yields.