Sorry, not all other countries use the parliamentary system.
Almost half the countries on Earth use another form of government:
http://en.wikipedia.org/wiki/List_of_countries_by_system_of_government
The chart, unfortunately doesn't really explain about the type of Republic, it's focused on the executive.
I will be more specific. Most of the other advanced Democracies are parlimentary, and in particular the ones that are famous for having 3 or more parties. Here are some expamples:
Canada
Israel
Japan
Great Britain
France
Germany
Italy
Those are the countries I am most familiar with. I'm not saying that they all have the exact same rules, but none of them are much like ours, and they are comparitively much more like each other.
In Canada only the House of Commons is elected. Senators are appointed. The House elects by district (called ridings).
So there House is a lot like our House in terms of the mechanics of elections (single individual per district is elected, first past the post race), but because it is a parliamentary system the Prime Minister is chosen by the House, and a majority (not a plurality) of MP's is needed to elect him, so third parties can get real clout.
If a bunch of Western States elected Freedom Party candidates it would have no impact on who was POTUS, but I guess it could make the organization of the house interesting. The Speaker could be a coalition candidate. Canada does have more than two parties in Parliament
In Germany any party that gets 5% nationwide gets some seats in Parliament, even if they don't win a district. Here is the Wikipedia entry on it
Bundestag The Reichstag building, seat of the Bundestag The Bundestag (Federal Diet) is elected for a four year term and consists of 598 or more members elected by a means of mixed member proportional representation, which Germans call "personalised proportional representation." 299 members represent single-seat constituencies and are elected by a First Past the Post electoral system. Parties that obtain fewer constituency seats than their national share of the vote are allotted seats from party lists to make up the difference. In contrast, parties that obtain more constituency seats than their national share of the vote are allowed to keep these so-called overhang seats.
In the current parliament (elected in 2009) there are 24 overhang seats, giving the Bundestag a total of 622 members. A party must receive either five percent of the national vote or win at least three directly elected seats to be eligible for non-constituency seats in the Bundestag. This rule, often called the "five percent hurdle", was incorporated into Germany's election law to prevent political fragmentation and strong minor parties. The first Bundestag elections were held in the Federal Republic of Germany ("West Germany") on 14 August 1949.
So that was my main point. Most of the countries that have 3rd parties have pretty different electoral systems that tend to foster 3rd parties (Germany) or at least make them potentially relevant (Canada). Our system seems to favor two parties.