What would happen if a government does not honor a ruling made by a judge?
An example would be US President Trump's Travel Ban, which was recently suspended entirely by a federal judge.
Note: This question is for worldwide politics. (The information I gave is just for an example/context).
In Europe definitely the court decision would prevail.
If we take Russia from where I am, the court decision would prevail over the government definitely especially regarding such not-so-important issue. It will prevail automatically: every person on duty will follow the court's decision rather than other regulations. Not following a court decision is a crime.
I want to point out that in modern Russia the judges are heavily dependent on the president in their career, so they are highly unlikely making decisions against the president. But they make the decisions against the government and ministries routinely.
In 1993 there was a case where the Constitutional court decided that the president violated the Constitution by disbanding the legislature and should step down. This led to a major constitutional crisis involving tanks firing on the legislature building. The president made a coup, enacted new constitution, the head of the constitutional court was fired (ironically, now he is the head of the constitutional court again thanks to his principled position that time).
So, for Russia the answer is: the courts will prevail or there will be a major constitutional crisis involving tanks firing in the capital.
In a democracy where rule of law prevails, the executive has to follow judicial decisions. People have the right to address the judiciary if they feel that the executive doesn't give them the rights the legislative wants them to have.
People getting their rights restricted by government officials acting against the law is not uncommon. The law is complex and a government official aren't legal professionals. Police officer might stretch the limits of when to use how much force, a tax bill can have a calculation mistake or an immigration officer might reject a person without a legally valid reason to do so.
When this happens, the person whose rights got violated has the option to go to court. The court will then decide if this specific action by the government official was lawful or not. When the court finds that they were not, the actions taken by the government official will be reversed. The courts might also rule that the government officials who executed the order get sanctioned and/or that the government needs to pay reparations.
So what would happen if a government organization would repeatedly and systematically act against the law?
Lots of court cases, lots of cost for the tax payer, and in the end all their actions would be annulled by the courts anyway.
