Like many villains Luffy has met, Crocodile is confident in himself and in his abilities (Although, unlike previous villains such as Don Krieg, Crocodile's confidence comes from skill and power. His power is shown when he beats Luffy twice, nearly killing him both times). However, due to his confidence, he underestimated Luffy's willpower, which eventually led him to his defeat. His willingness to kill displays his cold-hearted nature and will not think twice about sentencing another to death. He is also very quick to anger if someone insults him in any way as seen when Sanji insults him over his Den Den Mush. 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. Luffy had called him stupid. He then bites his cigar in half and threatens to kill Robin for laughing at the comment.
He also lacks almost any code of honor and does not see the point in offering those who about to die a chance of dying honorably.  One of the few signs of honor he displayed at all was in his third fight with Luffy. He states that Luffy deserves an honorable death from his venomous hook. However, due to the situation at the time of battle, this could be considered more an act of cruelty than honor. However, it's also possible that due to the fact that he almost never fights with his poison hook, it is a tribute to Luffy's tenacity, as he stated himself. He also has a habit of often using the term "worthless" to refer to the desperate struggles of his enemies.
Crocodile has shown to be extremely cynical and cold-hearted. He displays complete disregard of the "romantic" pirate lifestyle, stating that all the things the Pirate King once had mean nothing to him. He places more importance in military power. Crocodile believes that only ignorant fools declare their grandiose dreams. Several times, he refers to trust and faith in others as idiotic. He has stated that he has done away with countless people like that. He goes so far as to mock those who fight for others, making their defeats to him all the more harsh.
If Crocodile is extremely angry or annoyed with his victim, he will rarely kill them outright, often leaving them for dead and suffering. 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 is the only reason Luffy lived through any of his fights with Crocodile.
He may very well have been the same happy, carefree person as Luffy once. They even shared the same dream. Despite this, his time in the Grand Line has corrupted him and jaded his personality, causing him to turn into the cruel person he is. His time in the Grand Line also caused him to let go of his dream.
Apparently, after losing to Luffy and stripped of his title of Shichibukai, Crocodile lost interest of the outside world. This caused him to not escape with the rest of his subordinates during the breakout, and eventually to his transfer to Impel Down. His only motivation to leave Impel Down was for a chance to kill Whitebeard. He also seems to have mellowed out a small amount since his defeat. He does seem more willing to help others (when he offers to help Luffy escape from Impel Down). He will even accept help from others. Although, it was probably because the help from others benefitted him. Before he went to Impel Down, he wouldn't care if his allies were being killed. He might have even killed them himself. However, in Impel Down, he goes back to help his allies as they were being decimated by the Demon Guards.
One of his most notable personality traits, besides his seemingly limitless evil, is his complete and utter lack of fear and doubt. He is often very composed. He only rarely loses his temper (one of these occasions would end up costing him, helping toward his final defeat). Upon his capture, he simply disregarded the notion of escaping simply because he didn't "feel like it.". Similarly, he smiled at the news that he was to be sent to Impel Down, and has appeared unshaken during his stay there. Crocodile is, in fact, one of the very few prisoners seen completely unaffected by the tortures and conditions of Impel Down (along with Mr. 1). He is also the only one who appears to be enjoying himself (he is initially seen smiling and mocking his fellow prisoners). Crocodile says that he was in Impel Down because he chooses to stay. He only decided to leave only because of the chance to kill Whitebeard, Crocodile appears to act largely on whims and selfish desires. He simply "goes with the flow". He is unaffected by what happens when he does not act on these desires.
CrewCrocodile's connection to Robin was a strictly business-related one; he did not consider her a friend, only a tool for his own ambitions. He never once showed her compassion; she was just expected to follow orders. He held no pity for her when she failed to deliver Pluton and didn't think twice about striking her, although he did admit she had been a good partner to him moments beforehand.
He also did not refrain from acts of cruelty towards the other Baroque Works Agents under his employment, especially those who failed him (ex. feeding Mr. 3 to his Bananawani), However unlike previous villains such as Kuro, he doesn't harm subordinates for no reason, he strikes out at them if they fail or if they betray him.
Despite his cruelty towards his subordinates, he still manages to get some level of loyalty out of them after his defeat, as demonstrated in Miss Goldenweek's attempt to save him and the other Baroque Works agents and in Mr. 1 staying with him in prison. He later reward this loyalty by releasing Mr. 1 from his cell when he escaped.
He was also acquainted with Emporio Ivankov during his rookie days. Ivankov is also knowledgeable enough of Crocodile to know his weakness.
Despite his cruel attitude, he does show some level of concern or at least responsibility for his allies as seen when he turned back with Luffy and Jinbei to help their allies who were almost killed by the Demon Guards of Impel Down although he did it with a level of annoyance.
EnemiesCrocodile is an enemy of Arabasta because of his attempt to conquer the country. He especially is on bad terms with Vivi for the chaos and crimes he committed towards her father and country. As of the end of Baroque Works he is now an enemy of the Marines and the World Government for potentially causing a rift to form in the balance of the 3 Great Powers of the world. He remains a major enemy of the Straw Hats and his defeat at their hands is considered one of their greatest achievements.
He also has some type of grudge against Whitebeard. Although not fully explained, he comments on how he wishes to go and fight Whitebeard himself so he could kill him.
When Crocodile was still a rookie, he met with Emporio Ivankov, who learned of a "precious weakness" of his.
Abilities and Powers
Crocodile is one of the strongest characters in the series, as well as a (former) Shichibukai. He was the Shichibukai with the second lowest bounty at the time, Hancock having the lowest, and they are likely to be the only one's known to have a bounty of less than Beli100,000,000 (excluding Blackbeard), although had his bounty represented his threat level at the time he met Luffy, it would have more than doubled and broken the Beli100,000,000 mark.
Indeed, when Crocodile was stripped of his Shichibukai status and was transferred to Impel Down, he was placed in Level 6, where the world's absolute worst criminals are kept. He is also one of the few people to be able to take a "baptizing" in boiling water in Impel Down without flinching, which is considered an impressive feat. During Luffy's breakout of Impel Down, Crocodile is the only one of the three (along with Luffy and Jinbei) who did not sweat from the intense heat of Level 4.
He is extremely intelligent and cunning (one of the smartest in the series) which is apparent from his ability to mastermind Baroque Works while at the same time keep the World Government completely in the dark about what he was doing while making himself a hero of the people. He also has a skill for making flawless plans and seeing things that most other people wouldn't notice and deduce a correct conclusion from nearly no information (ex. seeing the white wrapping on the Straw Hats arm and almost instantly figures out it is a safe guard against Mr. 2's infiltration).
He also seems to have a better understanding of Devil Fruits than most people. This is seen in the mastery of his powers. This is also seen when he revealed the Four Demon Guards were actually "Awakened' Zoan fruit users. Other people were unaware that they were even Devil Fruit users.
Despite his powers being of the Logia-type where he turns into sand to avoid injuries, he is fairly resilient. He was able to take a serious beating from Luffy in their 3rd battle while he delivered attacks of his own. He is also able to survive falls from great heights with no long lasting damage.