In Julius Caesar the play, why should the senate be prevented from crowning Caesar? Why should Caesar not be crowned? What dangers would it pose if...

The senators feel that if Caesar is made king he will destroy them all and Rome along with them.

It is unclear whether or not Caesar wanted to be king.  Shakespeare presents us with a contradictory case. On the one hand, he refuses Mark Antony’s crown. On the other hand, he seems to agree to go to the senate meeting only after a crown is offered. That is circumstantial, though. He might have just wanted to stop the senate from crowning him.

To the Romans, there is nothing worse than having a king.  While Caesar was dictator, this limited his powers and meant that the senate was still in power and had some power over him. The senators who conspire to kill Caesar are doing so because they feel that Caesar would be dangerous if he were king, and had no one to check his power.

Brutus explains in his soliloquy that Caesar has done nothing yet which indicates that he is a danger to Rome, but he has indicated that he is ambitious. They fear that ambition.

I have not known when his affections sway'd
More than his reason. But 'tis a common proof,
That lowliness is young ambition's ladder,
Whereto the climber-upward turns his face;
But when he once attains the upmost round.
He then unto the ladder turns his back,
Looks in the clouds, scorning the base degrees
By which he did ascend. (Act 2, Scene 1)

There’s the problem.  Caesar may decide that he wants more, and pay no attention to the people who helped him get into power.  He may step all over all of them in his desire to get full control of Rome. This is what Brutus and the others fear. Brutus knows Caesar well, and he has so far not seen him do anything against the good of Rome. However, Caesar has been walking a fine line. Who knows what he would do with that much power?

In Gaul and in the war against Pompey, Caesar came too close to making himself king for the people’s comfort. He made the Romans rich in Gaul, so no one complained. The war with Pompey was Romans against Romans, however.  Pompey was his son-in-law and should have been his ally.  For Caesar to make war against Pompey was unforgivable to some Romans. This is especially true of those who supported Pompey and found themselves on the wrong side when Caesar won, including Brutus and Cassius.

Thus, when Brutus and Cassius and the others decided to kill Caesar, it was in the name of Rome. They believed that ending Caesar would end the threat to Rome. Caesar had not done anything yet, but if he was king he would have absolute power and no one could stop him. The senators would be out a job.