Alright, this question is pretty broad of course, but I will try my best. I have extensively studied Vichy France and Germany, and thus I have been able to also gather a bit of info on Switzerland which might interest you. I don't know that much about the others sadly. Okay, here we go.

Switzerland

The Swiss population and Supreme Command had quickly grown into one of the most germanophobic in Europe, as according to J. Piekalkiewicz in his amazing comprehensive work on World War 2.

Piekalkiewicz accounts large parts of the Swiss independence and neutrality to be the work of Henri Guisan, General (which in Swiss terms means Supreme Commander) of the Swiss Army.

Guisan was very much aware of Hitler's pan-germanism and Mussolini's Greater Italian sentiment. Switzerland of course hosts a German, Italian and French community. Switzerland gave mobilization orders in September of 1939 and fielded between a quarter and half a million troops, fortifying the mountain ranges with bunkers and artillery positions. Switzerland called off mobilization after the Fall of Berlin.

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Trivial sidenote: Switzerland used Prisoners of War from the allied powers that fled from France across the border to escape the Germans in 1940 to build their new roads. The more you know.

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Guisan, himself Franco-Swiss, certainly didn't harbor any natural sympathies for either Mussolini or Hitler and their respective pan-nationalism. However it should be noted that he saw communism as the greater ideological threat than fascism and thus harbored sympathies for the ideology itself.

The Swiss people at large saw an existential threat in Germany and Italy. The NSDAP had established an AO (Auslandsorganisation, organization in a foreign state) in Switzerland in 1930, much akin to the one established in Austria that would later try to push the Anschluss from within.

The NSDAP/AO in Switzerland was headed by Wilhelm Gustloff from 1930 to 1936, a man most well-known for getting assassinated and having a ship named after him that would be sunk by the Soviets while trying to flee from East Prussia.

There also were internal Swiss parties with the German-völkisch ideology, the most notable ones being the Nationale Front and the Eidgenössische Sammlung. They scored their highest at the Federal Election in 1935, where the National Front gathered 13,000 votes, compared to the 255,000 of the Social Democrats, the 216,000 of the Free Democrats and the 185,000 of the Conservatives.

The crazier Hitler got and the more aggressive he acted, the less likely the Swiss people, even the German Swiss, were to support his völkisch and national socialistic ideals. German Swiss people, as well as their French Swiss and Italian Swiss eidgenossen, have always identified more with Switzerland than with their respective linguistic origin.

And Swiss people have always embraced their neutrality and isolation, be it in historical terms since the Congress of Vienna (which specifically declared Switzerland neutral after Napoleon had invaded it in 1803) or in contemporary politics. But we of course don't discuss those here.

Hitler had threatened the Swiss diplomatically since the summer of 1940. He claimed that the Swiss press, which enjoyed its freedom thoroughly by criticizing Hitler's expansionism, violated Swiss neutrality by giving the Swiss people a biased view.

Even in 1943 and 1944, Hitler and his generals considered attacking across the border, as according to Piekalkiewicz, because cities like Basel at the German-Swiss border were still lit even though the German cities were dark, thus giving the allied bomber squadrons a good idea where they were.

Switzerland, which had feared becoming the victim of being the flank that Germany used to breach into France (which indeed was a thought of the German High Command in spring of 1940), constructed the 'Reduit National', the national retreat, in the centre of its mountain ranges. The Swiss Army would retreat there to nominally keep Switzerland on the map and fighting should it get invaded. Public opinion of this last bastion of Swiss neutrality was positive.

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So, to sum it up:

TL/DR: The Swiss definitely viewed the nazis as the "bad guys". The question if they viewed the allies in reverse as the "good guys" cannot precisely be answered in my view however. Switzerland wanted desperately to keep its independence and to maintain neutrality. They viewed the Axis Powers as the aggressors and thus set up defences against them.

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Sources:

• Government of Switzerland: Election Results of Switzerland

• Piekalkiewicz, Janusz: Der Zweite Weltkrieg, in the version of 1985 [the IMO best book about World War 2 there is. If you speak German or Polish, get it.]

• de Weck, Hervé: Guisan, Henri; in Historisches Lexikon der Schweiz, 1998

• Zentner, Christian: Der Zweite Weltkrieg, 1981

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EDIT 1: Noticed that I made sound Guisan like an anti-fascist, which he likely was not. Provided additional information in that regard.

EDIT 2: Corrected the wording of the "mirrored Schlieffen Plan" passage.

I've posted before about Ireland's role during WW2. While officially neutral, there were some instances where they collaborated with or assisted the Allied powers. For example, "Plan W" was concocted by Ireland and the UK as a contingency of sorts in the event that Ireland was invaded by the Axis. If Ireland was successfully invaded, Britain would have been flanked on nearly all sides. (There was also planning by the Irish to be able to repel the British in the event that they invaded Ireland -- the issue being access to ports of course. The IRA were pro-Nazi mostly out of spite from what I understand.) On the whole, Ireland sided with the Allies, going so far as to share intelligence from time to time. More information on this is found in Robert Fisk's In Time Of War.

I also wrote about Iceland before as well. They were officially neutral but were occupied by the British in May 1940 during Operation Fork. The invasion was not met with much in the way of violence, but the government did protest about the violation of their sovereignty. The British only had a single casualty -- a marine committed suicide en route to the island and no one in Iceland was killed, though many Germans were arrested. Iceland of course was considered important by the British to protect the Atlantic sea routes, so the decision was made to invade (negotiating was risky since it could alert the Germans). Iceland cooperated with the Allies during the remainder of the war while maintaining official neutrality.

I cannot really answer for the OP's question, but for context it might be interesting to know that even in Finland, plenty of people - most likely sizable majority, although such things were not exactly polled - believed that the preferable outcome for the war would be a victory of the Western Allies. The details about concentration camps were not known publicly in Finland until after the war, so these beliefs were rooted in more general distrust of Hitler's regime and its policies.

Of course, there were plenty enough Nazi and/or German sympathizers (these were not the same things, although there was certainly overlap). However, in Finland at least - if I'm to believe sources I've read, such as Näre & Kirves's Ruma Sota, or my trusty Suomen historian pikkujättiläinen - the peak of Nazi sympathies had already passed in mid-1930s, and by 1939 the majority were either downright anti-Nazis or at least highly skeptical of Hitler's regime. This was exacerbated further by the Molotov-Ribbentrop pact and the Winter War, when Germany offered no help whatsoever and even prohibited arms shipments from Italy and other countries from reaching Finland. Needless to say, this combination was a major blow to remaining Finnish Nazi sympathizers, just as the Molotov-Ribbentrop pact and the beginning of the war had been rude shocks to many Finnish Communist sympathizers.

On the other hand, German sympathies most probably reached their peak after the beginning of the Continuation War in 1941, as, for a while, it seemed the German successes against the Soviet Union would help Finns to take back Karelia, and with interest to boot. These sentiments faded fairly quickly however, and the government's censors ultimately clamped down on overtly pro-German expressions in media: these were very problematic for a government that tried to retain diplomatic relations to Britain and the U.S. (In the end, after pressure from Stalin, Britain declared war on 6th December 1941; the United States did not, although it recalled its diplomatic mission at one point.)

From what I've gathered from reading Finnish history and in particular personal histories, I think that there really was an acute apprehension about the devil's bargain Finland had to make in 1941. The ethical, moral and practical problem of siding with Hitler while trying to defend what was very much a Western-oriented democracy and hoping fervently for (Western) Allied victory is evident from several memoirs and contemporary recollections, and although these are undoubtedly colored and somewhat exaggerated by the outcome of the war, I believe the underlying sentiments were authentic. Or, as my granddad put it to me much later, "we didn't like dictators one bit, and that's why we fought."

Does anyone have information for countries besides Switzerland? Maybe African or Asian countries that weren't directly involved in the war?

In Sweden, it differed. Rich people and the military/industry brass loved them, as did the right-wing sector of the entertainment industry. Regular people hated them, although when Finland was invaded it was the Soviet Union who became the big bad guy instead. Politicians mainly kept as quiet as they could. But that's still a gross generalization. Raoul Wallenberg was a rich businessman, and he saved the lives of thousands of Jews, and received a post-mortem "Righteous among the nations" award from Israel, as well as the congressional gold medal from the United States. Neutrality was a political decision, and the Nazis were monstrous warmongers, whose stated aim was to exterminate every Jew in Europe. Go figure what people thought of them.