It depends on the time and the place.
In France, the French government retained sovereignty over the whole country. After the Battle of France had been decisively lost in 1940, the French Prime Minister, Paul Reynaud, tried and failed to convince the rest of the cabinet to evacuate the government to Algeria or Britain and continue fighting from there. Reynaud resigned rather than carry out the cabinet's desire to sue for peace, and the President (Albert Lebrun) appointed Marshall Philippe Petain (the leader of the surrender faction in the cabinet) to replace him. Petain asked Germany for an armistice, which Germany granted on terms that amounted to a surrender. Among other provisions, Northern and Western France (about 60% of Metropolitan France, including Paris) would be occupied by Germany until a final peace treaty was agreed (it never was, nor were negotiations ever begun in earnest), and France would be assessed an exorbitant fee to pay for the occupation. The rest of France (including the colonies) would remain unoccupied under the direct control of Petain's government.
Petain set up a new capital in Vichy, a small resort town in the unoccupied zone. There, the French Parliament voted itself out of existence and granted Petain dictatorial powers (ending the Third Republic and establishing what we now refer to as Vichy France). In the unoccupied zone, citizens paid their taxes as normal, except they were sent to Vichy instead of Paris. In the occupied zone, the German military and the French civilian administration had overlapping jurisdiction: the French bureaucrats still nominally worked for the government in Vichy, but they were required by the terms of the occupation to follow the policies of the occupation authorities. In the occupied zone, then, taxes were still assessed according to French law, by administrators who worked for the French government, but they operated under the direction and supervision of the German military. In practice, this supervision seemed to be relatively light: Petain's government's policies were aligned enough with German interests, and the German occupation's administrative resources were small enough, that the Germans mostly let Vichy set policy for the occupied zone. In both zones, the taxes went to Vichy, and in accordance with the armistice agreement, Vichy paid Germany the agreed-upon costs of the occupation (which were much higher than the actual costs, so Germany turned a substantial profit).
In November 1942, after Britain, America, and anti-Vichy French exile forces ("Free France") successfully invaded France's North African colonies (Morocco, Algeria, and Tunisia), Germany executed Case Anton, occupying the remainder of Metropolitan France. The Vichy government remained in operation, however, and the French civilian administration continued running under German occupation.
Nazi-occupied Poland was divided up into two zones (plus a third zone in the East, which was annexed by the Soviet Union). Northern and Western Poland (a bit past the pre-WW1 borders of Imperial Germany) were annexed to the German Reich. They were integral parts of Germany, and were administered and taxed directly by the German government under German law and Nazi policy. The remainder of Poland was put under a special German occupation administration called the General Government, lead by a senior Nazi Party official (Hans Frank) who served as Governor-General of Poland. Frank and the other senior officials of the General Government ruled by decree, and they administered the territory mostly through imported German officials. The existing Polish civilian police were drafted into German service under German senior officers (mostly from the German civilian police) and used to help enforce the General Government's rule. The General Government collected taxes for its own internal use, and as with Vichy, they also sent a substantial portion of their revenue to Germany, officially as a reimbursement for the costs of the occupation.
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I am not familiar with France, but I can give you some tidbits about Poland. This relate to Polish occupied territories (mainly the General Government), as opposed to territories outright annexed into the Reich, such as Silesia. The latter is a completely different case.
First of all, mind that the entire occupation of Poland was geared towards maximization of economic drainage. Taxation was just part of it and not even a major one. If there was ever a plunder economy, this was it in its most pure form. Among other things, the occupying power took over the control of Polish industry and its output, even if it nominally remained under native ownership. Labor was mandatory and slave labor of Poles and Jews used extensively. Natural resources were ruthlessly extracted, and negative effects of deforestation that happened back then are felt even today. More often than not, the authorities simply discarded any semblance of law and simply plundered whatever they wanted. This took many forms and ranged from localized expropriations (often conducted on private initiative of local corrupt officials) up to state-organized wholesale theft of assets, such as "temporary" freezing (essentially taking over) of bank accounts, forced "exchange" of any foreign currency and bullion or confiscation of property left by victims of the terror (which included any property of Jews murdered in Holocaust).
In this environment, taxation played a minor role. Barring some exceptions, the Germans kept pre-war Polish currency. This economically isolated Poland from the outside world, because obviously currency of an occupied territory was essentially worthless on international markets. Monetary taxation therefore did not benefit Germany as a whole. It was used mostly for the needs of local German administration, which was more than happy to run printing presses and mints whenever it needed some more cash on hand. Although taxation was much higher on average than in pre-war Poland, it was nevertheless kept on a level relatively moderate by today's standards. I encountered a figure of 30% of an average income tax, though I am unable to verify whether that's median taxation. There was also a poll tax, a carryover from previous Polish taxation system. On top of those ordinary taxes, German authorities often introduced local extraordinary taxes which could've take any form. Such taxes were often used as punitive measures for perceived disobedience or for some especially shocking actions of the Polish underground. For example, a massive extraordinary bulk tribute (and hostages to ensure its timely payment) was levied upon the city of Warsaw after the underground assassinated actor-turned-collaborator Igo Sym. It was a big affair. Imagine an European movie superstar who became a turncoat and was killed by an assassination squad in his own apartment despite him being under high security protection.
Completely apart from monetary taxations were in-kind taxes. These were unknown in pre-war Poland and were levied upon farmers who were obliged to deliver part of their produce. The tax rate differed between provinces on basis of many factors, both objective (like soil quality or type of produce) and arbitrary. Over time the rates were continuously increased and late in the war reached whooping 60% of produce in some regions. The execution of this tax was often savage. Avoidance was punished even by death or sending into a concentration or labor camp. Villages which were as a whole considered to be uncooperative were often burned and their inhabitants were wither killed or sent to labor or concentration camps. Produce taken from Polish farmers was used to feed German civilians in Germany and German armed forces. As a result of this policy, by the end of the war Poland was entering famine conditions.
In the Netherlands, this has been researched by prof.dr Peter Essers from Tilburg University. He specializes in Tax Laws. There was a lot of tax evasion in the Netherlands in the 1930s and the Dutch tax administrations had come up with a plan to collect taxes via employers and revise the system completely. The Dutch government refused, as they were afraid that big companies would leave the country if they had to pay more taxes in a time of crisis. When the Nazis occupied the Netherlands the tax administration simply went to the new government with their plan and this time received a much more enthousiastic response.
The tax law was revised extensively and according to prof Essers, in the end the Nazis only needed 10 people at the top to make everything work like an oiled machine. There was some resistance from individuals, but according to him most employees were law-abiding and much more interested in the technicalities of their work than the ethics. The tax administration collected the taxes for the new government, installed by the Nazis, and that government transferred most of that to Nazi-Germany, so the people of the Netherlands didn't pay their taxes directly to Nazi-Germany.
Essers calls the situation more accomodation than collaboration. The tax administration wanted reforms that were denied by the Dutch government and simply took the opportunity to get what they wanted after the occupation. In an interview with the Volkskrant in 2012 after the publication of his book 'Belast verleden' (which can be translated as 'taxed history' but also as 'burdened history') he calls the actions of the tax administration 'bitter', 'shameful' and 'very gloomy' and says "A technocrat doesn't have to think or care about nuances. They apply the rules without considering the ethics".