In late September, Christophe de Margerie, the CEO of French oil major Total (TTE 1.10%), joined environmentalists against Arctic drilling in a chorus of "Don't do it, guys." De Margerie's statement made waves, as few recalled any time when big oil advocated not drilling something. Now, months later, a Royal Dutch Shell (RDS.A) Arctic drilling rig has run aground and must be rescued, marking the latest in a number of mishaps for Shell's efforts in the Arctic.

This ordeal may dissuade some companies from throwing their hats into the Arctic ring, but there are plenty of other offshore spots with unique challenges and potential riches to tempt big oil. Today we'll look at three of them: New Zealand, Cuba, and New Foundland.

New Zealand
We'll start with the land of the Kiwis, as the country's rough seas offer some of the same challenges that producers face in the Arctic. The Financial Times reported yesterday that New Zealand is making strides to increase oil exports in order to drive GDP growth. The country has already revamped its permitting process and is currently shoring up its regulatory framework to address health, safety, and environmental concerns.

This past December, New Zealand awarded 10 exploration permits good for five years to Shell and Anadarko (APC), among others. Right now, oil production in New Zealand comes from one basin, but there are at least 17 others that may prove commercially viable. Shell is currently conducting seismic surveys and will not attempt to drill until this summer or 2014.

Still, the offshore risk here can't be underestimated. Consider that New Zealand's worst maritime disaster happened on a calm night when a Greek cargo ship hit a reef and broke in half, spilling oil and cargo everywhere, and you get a sense as to what these producers are facing, even on a good day.

Cuba
The challenges to drilling offshore Cuba are political ones, but in this case they are almost as off-putting as Mother Nature.

The 50-year-old U.S. embargo of Cuba means that all sorts of ridiculous rules are in place that make drilling in Cuba difficult, and potentially dangerous. For example, all equipment used -- including the actual rig -- must contain less than 10% American-made parts. If there is an American-made part on the rig, say, the blowout preventer, and it breaks, the rig cannot be serviced by an American company. Even if it's the closest help available.

Naturally, should such an incident occur, the U.S. can override the law and allow for help, but basically whoever is drilling offshore Cuba is a foreign company using foreign equipment. And so far they have all failed miserably. Spain's Repsol tried in 2011 with a Chinese rig and came up empty. Malaysia's Petronas and Russia's Gazpromneft failed a year later.

Most recently, another Russian company, Zarubezhneft, decided to give it a try. The company showed up in mid-December with a Norwegian rig owned by Songa Offshore. Zarubezhneft is drilling in a shallower location than the previous attempts, hoping for a significantly better outcome. The company will drill for six months, and plans to announce its results in April.

The U.S. Geological survey estimates there are 4.6 billion barrels of oil offshore Cuba, though the country's own estimate has been as high as 20 billion barrels. Regardless, if and when a company drills a commercial well, the ensuing oil industry lobbying in Washington may open this game up a bit.

Newfoundland and Labrador
ExxonMobil (XOM -2.78%) recently announced its plan to drill offshore Eastern Canada's Hebron field. Exxon is spearheading the development, taking a 36% stake in the project while Chevron (CVX 0.37%), Suncor Energy (SU -0.08%), Statoil (EQNR -0.57%), and Nalcor Energy, will all have minority stakes ranging from 26% down to 4.9%.

Oil production will begin in 2017, but this project has actually been in the works since 2006. A disagreement regarding the construction of the drilling platform delayed the eventual go-ahead. The provinces are completely on board now, however, and looking forward to the royalties and job creation the project is expected to generate. Newfoundland's oil production is about 190,000 barrels a day currently, but declined significantly in 2012.

The field contains an estimated 700 million barrels, and Exxon anticipates production will reach 150,000 barrels per day. It will spend $14 billion on the project.

Foolish takeaway
The U.S. Geological Survey estimates that 25% of the world's undiscovered conventional oil and gas reserves are in the Arctic, the majority in offshore reservoirs. That means that despite the difficulties in accessing those resources now, there is too much potential for companies to simply give up. Expect exploration and production companies to hone their skills on the three plays mentioned above, and continue to make attempts to produce in the Arctic.