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No. 5: Ireland, 122% Debt/GDP

Kicking things off in fifth place is Ireland, one of the hardest-hit nations in the recession. The crisis slammed the country's GDP and devastated the country's economy; Irish unemployment still lingers above 14% five years after the depths of the recession. Despite the eurozone's recession, however, hope remains for Ireland: The European Commission expects Ireland's GDP to grow 1.1% this year, the third-fastest rate in the eurozone. By 2015, the IMF expects Ireland's unemployment rate to fall below 13% -- not good, but progress nonetheless.

Despite the bleak reality of the Irish economy, investors have capitalized on at least one of Ireland's top stocks. The Bank of Ireland (NYSE: IRE  ) has dropped nearly 98% over the past five years, but the stock has gained more than 92% over the past year. Should you invest in this beaten-down riser? Probably not. While this stock has done well lately, Ireland's recovery -- as well as Europe's -- is still too fragile to bet on risky financial picks like this. Stick to larger, less exposed, and less risky financial stocks in Europe if you're tempted by the sector's regional offerings.

Ireland's debt could fall out of the top 5 if the country's growth outpaces spending, but for now, the Irish economy's meager growth ranks among the leaders in one of the worst economic regions on Earth. That's not a sign that this debt will fall meaningfully soon, and the IMF expects Irish debt to remain above 105% of GDP by 2018.

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No 3: Italy, 130% Debt/GDP

Let's have a big hand for Italy, Europe's third-largest economy -- and the third-most-indebted top-50 economy in the world. While nations such as Spain and Cyprus have dominated the debt talk in Europe, Italy has slowly dug itself into a giant hole. By posting a seventh straight quarter of economic contraction to start 2013, Italy now finds itself in its longest recession since the country began keeping quarterly economic records in 1970. Throughout the turmoil, Italy's debt has steadily climbed, rising 10 percentage points in the last two years as the Italian government attempts to keep its economy from sinking even further.

There's little to like here for investors. The iShares MSCI Italy Index (NYSEMKT: EWI  ) ETF dove earlier this year with the nation's tumultuous election. While it has recovered since and has posted 30% gains over the past 52 weeks, the Italy ETF has lost 1.3% this year. Italy's economic woes and this ETF's performance aren't one and the same, however. If the European Central Bank continues to lower interest rates as it has in the past, this ETF could rise even as the nation's recession lingers on. However, Italy's a risky proposition at best, and with other, more stable markets surging, there's no reason to take a flier on this pick.

In short, don't expect Italy's debt to come down much in coming years -- nor should you expect its economy to please any economists. The IMF predicts Italian debt to fall less than 7 percentage points over the next five years.

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No. 1: Japan, 245% Debt/GDP

The world's most debt-burdened nation is also home to 2013's best stock market. Here's a debt crisis that investors can get behind.

Japan's debt isn't so much the product of recession -- as with the European nations above -- as it is a consequence of the country's two decades of stagnation combined with new Prime Minister Shinzo Abe's ultra-aggressive stimulus tactics. Abe's hope is that easy money will ignite the Japanese economy after years of sluggish growth, which would help ease this inordinately high debt. If the plan fails, however, Japan will be stuck with a monster debt just in time for an aging population to tax social systems to the brink. That's a bad combination for this economy's future.

In the meantime, however, investors have plenty to gain across the Pacific. Abe's stimulus is great news for the country's financial sector, and brokerage firms such as Nomura Holdings (NYSE: NMR) have capitalized on Japanese stocks' wild gains. With the yen weakening against the dollar, investors continue to pour money into Japanese stocks -- a cycle that will continue to fuel Nomura's success and reward the firm's shareholders. The company recorded its best quarterly profit in seven years last quarter, and while Nomura's stock certainly isn't cheap right now, it has a bright future so long as this rally continues.

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