In his remarkably insightful observation of Cassius in Act l, scene ll, Caesar expresses the following sentiment to Antony:
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.
Using metaphoric references, Caesar juxtaposes what he sees in Cassius with that which he wishes to be surrounded with. He wants to be accompanied by men who are at peace, comfortable with their lot and who, therefore, pose no threat to him. His reference to Cassius's 'lean and hungry look' implies that Cassius is desirous of something more and is on the prowl for something to feed his ambition. The extended suggestion is that in the process, Cassius is constantly plotting and figuring out a means to achieve his desire. He sees Cassius as dangerous in this regard, since one does not know what he is planning or what, exactly, he wishes to achieve.
Caesar ignores Antony's assurance that Cassius is not dangerous; Antony says Cassius is noble and pleased with his position. He tells Antony that he would have preferred it if Cassius were more corpulent, since one assumes that those who are somewhat larger in size are happy. Cassius indeed does not look satisfied or happy. Caesar emphasizes his point by stating that Cassius does not indulge in the arts or enjoy music. He hardly ever smiles, and when he does, his grin is scornful, as if he regretted smiling in the first place.
He furthermore states that men such as Cassius are never at peace when they behold those who are greater than they, suggesting resentment and envy. It is this, Caesar asserts, which makes such men dangerous. The insinuation is that since they cannot accept that others are their superior, they would either want to get rid of them or usurp their position.
Caesar informs Antony that he would rather tell him about what one should fear than what he himself is afraid of. He had previously stated that he does not fear Cassius, per se, but that he fears the danger Cassius represents. It is quite evident that Caesar does harbor deep suspicions with regard to Cassius, but he obviously does not want Antony to assume a weakness in him and, therefore, asserts his authority--he is, after all, Caesar the indomitable.
It is ironic that Caesar expresses these sentiments here for it is indeed Cassius who is the chief plotter in his downfall. Caesar's speech foreshadows the events which will later result in his assassination. For the same reason, further irony lies in the fact that Antony defends Cassius. Moreover, it is also ironic that the general, for all his suspicions, does not take any action against Cassius, such as having him observed or spied upon. The general is, unfortunately, so confident in his position that he deems himself invincible--a factor which adds to the irony.
Caesar has noted a restlessness in Cassius that indicates that Cassius becomes easily discontented and jealous when dealing with those who have done better in life than he has. In a long discussion with Mark Antony in Julius Caesar Act I Scene 2, Caesar specifies exactly why he feels Cassius is dangerous. Beginning with the somewhat shallow-sounding observation that Cassius is too lean and "thinks too much," criticisms that make Caesar look silly, he moves into a more substantiative critique:
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.
Such men as he be never at heart's ease
Whiles they behold a greater than themselves,
And therefore are they very dangerous.
In short, Caesar claims that Cassius is a jealous and cynical obsessive, who will automatically become restless and hostile when he sees someone who is superior to him. Since earlier in the scene, we have observed Cassius working on Brutus to turn him against Caesar, Caesar's words appear extremely perceptive.