Personality

Crocodile is confident in himself and in his abilities (Crocodile's confidence comes from his own skill and power. His great power is shown when he beats Luffy twice, almost killing him both times), and enjoys toying with his opponents, often smiling smugly when facing an opponent that he knows is weaker than him. However, due to his confidence, he seriously underestimated Luffy's willpower, which eventually led to his defeat.
His willingness to kill shows his cold-hearted nature and he will not think twice about sentencing another person to death. He is also very quick to anger if someone insults him in any way. This is seen when Sanji insults him over his Den Den Mushi. Crocodile comments that anyone who has ever insulted him, has been killed by him. This is also shown later in his first fight with Luffy where Luffy had called him stupid. He then bites his cigar in half and threatens to kill Robin for laughing at the comment.
However, he has a habit of insulting others and frequently uses the term 'worthless' to refer to the desperate struggles of his enemies. Although he has referred to many of his opponents' struggles as worthless in the past, he hasn't referred to his opponents' struggles since he first fought Luffy. He will usually insult others and generally say that they are not in his league; whether he's fighting a rookie or fighting a fellow Shichibukai (namely Donquixote Doflamingo who had a former bounty almost 300,000,000 higher than his own).
If Crocodile is extremely angry or annoyed with his victim, he will rarely kill them outright. He often leaves them to suffer until they slowly die. This proves to be a bad habit of his as it lead to his defeat. In his first and second fight with Luffy, instead of killing him, Crocodile leaves Luffy to suffer. This allows Luffy to come back and finally defeat him. This habit and sheer luck itself are the reasons Luffy lived through any of his fights with Crocodile. This also led to Galdino (Mr. 3) surviving the attempt by Crocodile to feed him to the Bananawani.
Crocodile shows no care for any of his subordinates. He is fully willing to sacrifice them to achieve his goals (such as Operation Utopia, where the entire Baroque Works would have been killed by the resulting cannon blast), or if they insult or fail him (such as Mr. 3 and Nico Robin did). He felt no true attachments to these people and only views them as pawns. However, the few that are strong earn his respect. The prime example is Mr. 1, whom Crocodile went out of his way to rescue from his cell.