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It is amazing Switzerland was able to stay neutral. It is not just a matter of choice and only up to Switzerland. Each side of the warring faction can take this hard stand "If you are not for me, then you are against me". Besides, Switzerland is in the middle of the warring action geographically.
How did Switzerland remain neutral? It is an amazing feat.
By not being a threat, and having no strategic benefit to either side worth fighting a professional army on excellent defensive terrain.
Take a good at Switzerland and you'll notice one thing: mountains. Lots and lots of tall mountains. Mountains mean easily defended choke points. They mean peaks hiding guns and observers who can call down fire and artillery upon the valley below. Mountains mean bad, narrow roads making moving and supplying an invading army difficult. These natural defenses, and the Swiss will to defend it, makes any attack on Switzerland very costly.
There must be a strategic benefit to attacking a neutral country. The low countries of Belgium and the Netherlands were invaded because they're a nice, flat highway between France and Germany to side-step Franco-German border defenses. In contrast, Switzerland is a country of natural defenses. Attacking Switzerland is charging into the teeth of strong defenses, exactly what you don't want to do.
If one side attacks Switzerland, they have to fight not only the Swiss army in mountainous terrain, but risks the opposing side reinforcing them as well. Now you've just lengthened your lines, opened a new and costly front, while giving your enemy excellent defensive terrain.
Specifically, at the start of WWI the Swiss fully mobilized bringing about 220,000 men ready to defend Swiss neutrality. With strong ties to both the Germanic Central Powers and the French, and with it becoming clear that the Western Front would be fought in the north, it mostly demobilized.
Again when the war clouds loomed, the Swiss increased their military spending and modernized their army. Again at the start of WWII the Swiss mobilized against invasion with over 600,000 men.
While Hitler assured the Swiss he would respect their neutrality, they were no dummies and saw Germany might attempt to absorb them as a Germanic state. In 1941 Hitler would tell Mussolini:
Switzerland possessed the most disgusting and miserable people and political system. The Swiss were the mortal enemies of the new Germany.
While the Germans mulled invading Switzerland in Operation Tannenbaum, a feint in the north with the Italians attacking from the south, his professional officers didn't like their prospects. Chief of Staff of the German Army Franz Halder said:
Jura frontier offers no favorable base for an attack. Switzerland rises, in successive waves of wood-covered terrain across the axis of an attack. The crossing points on the river Doubs and the border are few; the Swiss frontier position is strong.
Despite Hitler's desire to squeeze the "pimple on the face of Europe", no invasion happened. My guess is, like many other German plans after the fall of France, it got lost in the all consuming invasion of the Soviet Union.
Adding to @Schwern's great answer,
The Swiss Confederation had been internationally recognised as an independent neutral state at the Peace of Westphalia in 1648. During the Napoleonic Wars it failed to remain neutral, as some cantons had been annexed into other states and, under French influence, the Act of Mediation was signed and the Swiss Confederation was replaced by the more centralised Helvetic Republic which was allied to France. With the fall of Napoleon Bonaparte in 1814, the Cantons of Switzerland started the process of constructing a new, less centralised constitution.
It's not a big secret that some of the most powerful people in Europe including Hitler hid their ill-gotten money and gold in the banking system of Switzerland. It was the safest place in Europe thanks to its neutrality and very strict privacy policy of Swiss banks. Attacking Switzerland was like attacking your own house where you store your money and gold. It's better for them to keep it as their personal safe than burn and destroy it.
Switzerland is not located in a strategically important position which might help other countries get resources and labor. Both its land and population were too small to be a high-priority target.
Even if it remained neutral in WW II, it actually engaged in some military actions as the Wikipedia link on Switzerland indicates.
During the war, the Swiss Air Force engaged aircraft of both sides, shooting down 11 intruding Luftwaffe planes in May and June 1940, then forcing down other intruders after a change of policy following threats from Germany. Over 100 Allied bombers and their crews were interned during the war. During 1944–45, Allied bombers mistakenly bombed a few places in Switzerland, among which were the cities of Schaffhausen, Basel and Zürich.
