There wasn't a German resistance in the same way or scale that we might talk about the French Resistance or the Polish Resistance, but that doesn't mean that nobody resisted. There were many groups and individuals within Germany who tried to resist the Nazi regime.
Part of the problem when talking about resistance in a German context is actually defining what resistance is. In popular media, the idea that we have of resistance and Frenchmen and women wearing berets and blowing up railway bridges and gunning down Gestapo officers in the street, or the Polish Home Army organising a city wide uprising in Warsaw. None of that went on in Germany, and the most explosive events failed to kill Hitler or achieve their aims.
The main issue with trying to compare resistance within Germany to resistance movements in occupied countries was that in France, Norway, Denmark, Poland and a dozen other countries across Europe, the German occupation forces and whatever collaborationist governments they set up were illegitimate invading forces with no democratic legitimacy. In Germany, Hitler and the Nazi party were the (more or less) democratically elected Government. While their brutal oppression of their own people and subversion of democracy turned many against them, they were still the legitimate government of Germany. It takes a much larger psychological step to try and overthrow your own government than to resist against a foreign invader. This step became even more significant following the invasion of the Soviet Union and the beginning of what the Nazis framed as a war of annihilation against the evil bolsheviks.
That is not to say that Germans, both ordinary and elite, did not resist. The issue is how to characterise that resistance. While being defeatist and criticising Hitler in private, and trying to blow him up are both acts of resistance; that is, acts taken against the regime, they are completely different in terms of scale, effort and danger. The historian Detlev Peukert developed a pyramid model, where acts of resistance were classified on an ascending scale, both of severity and risk.
The Nazi party attempted to achieve total control over, and expected total obedience from, the German people. It intruded into every aspect of life, from Church to school to social life. In doing so, it caused significant resentment and opposition. At the bottom of Peukert's pyramid were both the most common and least impactful acts of non-conformity.
The Historians of the Bavaria Project, which looked at Resistance and Persecution in Bavaria over the course of Nazi rule adopted the following definition of resistance at the start of their studies:
Resistance is understood as every form of active or passive behaviour which allows recognition of the rejection of the National Socialist regime or a partial area of national Socialist ideology and was bound up with certain risks.
Any act which defied the Nazis' aim of total societal control was an act of resistance. This could be something as simple as refusing to give the Hitler salute or criticising the regime among friends. This carried relatively little risk, although the risk of denunciation was ever present. However, it denied the Nazi party control over the person.
It is important to note that those who offered acts of non-conformity were not die-hard opponents of the regime. Indeed, those who refused to conform in some ways might actively support the regime in others. A farmer who complained about the Government interfering in farming matters might support the expropriation of Jewish land, or a young person who fought back against the strict discipline of the Hitler Youth might support the 'reclaiming' of lost German territories.
Moving up the scale, we find protest against the regime. Although it can take many forms, protest is more visible and thus more dangerous. However, it does have a greater effect in opposing the regime. The following three examples give a good idea of how protest as resistance works:
One of the most famous images of resistance is this picture taken at the Blohm and Voss shipyards in 1936. In it, a man, believed to be August Landmesser, is refusing to give a Hitler salute. I mentioned previously that refusing to give a Hitler salute could be considered an act of non-conformity, but the refusal here becomes an act of protest given that it is in a crowd, and with cameras present.
Another famous civilian protests was the Rosenstrasse demonstrations in 1943. In response to the arrest of their Jewish husbands, a crowd of several hundred non-Jewish women gathered outside the building on the Rosenstrasse where they were being held, demanding their release. The very public nature of this protest saw it gain significant attention in the press. None of the women faced any negative repercussions for their protest. The Holocaust Museum has a page where you can read more about the demonstrations here.
A number of senior army officers protested against war crimes carried out by the SS and Wehrmacht, and orders which they believed to be criminal. General Johannes Blaskowitz, who commanded the 8th Army during the invasion of Poland, wrote in November 1939 in response to the actions of the SS in Poland: "the troops … refuse any association with these Einsatzgruppen which are working almost exclusively as execution squads". He described the actions of the Einsatzgruppen as ‘atrocities’. Similarly, in March 1941, upon recieving the infamous Commissar Order, Henning von Tresckow convinced Field Marshal von Bock to send another staff officer to protest to Hitler about the illegality of the order. However, when the staff officer arrived, he was told it would be unwise to raise the issue again as Hitler, in a towering rage, had already thrown an inkpot at another General who protested.
We can see the ineffectiveness of protest at actually changing Nazi policy. While there was a widespread public outcry against the murder of disabled people in the Aktion T4, sparked by fiery sermons from the Bishop of Munster, it did not limit the Nazis' murderous aims and intentions. However, it was nonetheless resistance against the regime and its aims. Furthermore, protest could be an important stepping stone towards active resistance. Henning von Tresckow would later be responsible for three serious attempts on Hitler's life.
Closer to the top of the scale we have active, political resistance. Again, this didn't necessarily have to be violent. Yad Vashem honours 627 Germans as 'Righteous Among the Nations', for risking their lives to save Jews from the Nazis. Very few of these actions were violent. The German intelligence officer Hans von Dohnanyi, for example, smuggled 14 Jews into Switzerland by disguising them as German agents. Other acts of political resistance included Otto and Elise Hampel, who wrote postcards critical of the regime and left them lying around Berlin, or Sophie and Hans Scholl, who were part of the White Rose student movement. There were also widespread communist resistance groups.
Political resistance was dangerous. It carried significant risk of arrest and death. None of the five people I named in the paragraph above survived the war. The communist resistance groups were often infiltrated by the Gestapo and their members executed.
Finally, at the top of the scale, and by way of a very long diversion, we reach what you've asked about. There was only one group who was working to kill Hitler and take down the Nazi regime for good. That was a group of German army officers who detonated a bomb in a staff meeting with Hitler on the 20th of July 1944. An honourable mention also goes out to Georg Elser, a lone wolf assassin who almost succeeded in blowing Hitler up in 1939 during a visit to Munich.
Army Officers had been trying to kill Hitler since 1938, when a plot was hatched to depose him, with a smaller subplot to kill him during the coup, if the Sudetenland Crisis caused war to break out. Their plots died down after war actually broke out in 1939, and only began again following the invasion of the Soviet Union, when a combination of witnessing the atrocities on the Eastern Front and the realisation that the war could not be won inspired the officers to try again. The most prolific group of these officers was in the General Staff of Army Group Centre. They were responsible for having a live, armed bomb in Hitler's presence on two separate occasions: once in a package disguised as a parcel of brandy and once in the form of a suicide bomber. On both occasions Hitler escaped unharmed and the bombs were not detonated.
The officers finally succeeded in detonating a bomb and launching their coup attempt in 1944, but Hitler was not killed and the coup failed. Most of the officers killed themselves or were executed, but a notable few survived.
Resistance was not just limited to one level of the pyramid. One of the best examples of progressive radicalisation is the Edelweiss Pirates, a group of young people who resented the strict discipline of the Hitler Youth. They went from skipping meetings and listening to banned music to eventually getting into street fights with the Hitler Youth and pushing allied propaganda leaflets through letterboxes. While the Nazis were initially reluctant to crack down on them, viewing them as a fringe irritant, eventually many members were sent to concentration camps, and a number were publically hanged.
Very little active, armed resistance against the Nazi regime took place. The means, motivation, and opportunity to do this were lacking for a large proportion of the population. However, resistance against Nazi aims and methods had many facets and many faces.