Why doesn't Caesar trust Cassius in Julius Caesar?

Caesar does not like Cassius because he is too lean, thinks too much, reads too much, does not like plays, and never smiles sincerely.

Caesar may not have known that there was a conspiracy to kill him, but he did not like Cassius.  He explained to Antony why he was suspicious of him.

Let me have men about me that are fat;
Sleek-headed men and such as sleep o' nights:
Yond Cassius has a lean and hungry look;
He thinks too much: such men are dangerous. (Act 1, Scene 2)

Cassius looks lean and hungry, but this is a metaphor for ambition. When Caesar says that Cassius does not sleep at night and thinks too much, it is not hard to infer that he means that Cassius might be planning something.  Caesar may or may not know what it is, but he does not trust Cassius.

Caesar has a few other reasons for not liking Cassius.

He reads much;
He is a great observer and he looks
Quite through the deeds of men: he loves no plays,
As thou dost, Antony; he hears no music;
Seldom he smiles, and smiles in such a sort
As if he mock'd himself and scorn'd his spirit
That could be moved to smile at any thing. (Act 1, Scene 2)

In addition to thinking too much, Cassius reads too much and watches people carefully.  He also does not like plays and never smiles unless he is being mocking.  The reference to plays and the smile means that Cassius is serious and committed.  Again, he is too ambitious.

Indeed, Cassius is determined.  He is the leader of the conspiracy to assassinate Caesar, and he is very careful to make sure that he hangs out with Caesar still and does nothing suspicious.  It does not work.  Caesar is too good at judging character.  The two men are on the opposite sides of the political fence, and Caesar needs to be suspicious of everyone.