Germany has a system of what it calls a vote of constructive no-confidence. Under that system, the opposition can build up a majority and on that basis alone pass a vote of no-confidence in the government—and replace it. In the ’80s, Helmut Schmidt faced such a vote of constructive no-confidence over the deployment of Cruise and Pershing missiles in Germany. The Liberal party then quit the coalition and joined the Conservatives to bring Helmut Kohl into power.
In fact, a ruling government need not be thrown out even if it loses elections—in any country in Europe. In Austria, two coalition parties came in with a majority a year ago. But the coalition of conservatives and rightists could not agree on appointment of ministers. So, the old caretaker government stayed in power till the two partners were able to resolve their differences and form a government.
The European models ensure that the President, or the equivalent head of state, does not have to order elections just because there is no alternative to a minority government. Since there is no advance guarantee that elections will yield a majority, you cannot simply go on having elections. The minority government simply continues in power. A lame duck government, but at least a government.
No country has seen coalition governments change more than Italy. The prime minister is voted out when a faction of his party or coalition defects. Normally the new majority (comprising members of the defecting government and the opposition parliamentarians) chooses a new prime minister within a few days or weeks. This has happened many times in the last few years. During his first mandate, Prime Minister Silvio Berlusconi lost the support of Lega Nord, which placed him in a minority situation. A new majority elected Lamberto Dini as prime minister.
If the opposition cobbles a majority and forms government, it can ask for elections to secure popular and moral justification for itself. But this too doesn’t happen often. Elections are held when due, though there is usually some flexibility allowed to the ruling government. In Britain, at least, the prime minister can seek an early election, and many see this as giving the ruling formation an unfair advantage.