As a former Warlord of the Sea, Crocodile is powerful enough to be recognized by the World Government. He was the Warlord with the second lowest bounty at the time (81,000,000), with Hancock having the lowest, although he held the title for so long that such a low bounty would now be outdated. Indeed, when Crocodile was stripped of his Warlord status and transferred to Impel Down, he was placed in Level 6, where the world's absolute worst criminals are kept.
He defeated Luffy no less than twice before his eventual defeat. In fact, if not for his good luck and the help he received from several people, Luffy would have been killed in all three battles: he was impaled (and then rescued by Nico Robin), dehydrated (and then revived by his own Water Water Pistol), and poisoned (and then received the antidote from Robin). Moreover, if Luffy's blood had not served as a way to nullify Crocodile's Logia-Type defense, and if Robin had not supplied Luffy with the antidote to his hook's poison, the third battle would have effectively favored Crocodile as well.
Despite his powers being of the Logia-type, allowing him to turn into sand to avoid injuries, Crocodile has an enormous amount of physical stamina, durability, pain tolerance, resilience and endurance, coupled with remarkable speed and reflexes. He was able to take a serious beating from Luffy in their third battle while countering with attacks of his own, and he later managed to take a direct strike from a diamond-encased Jozu with only a single burst blood vessel. He is also one of the fewpeople known to tolerate getting "baptized" in boiling water in Impel Down without flinching, which is considered an impressive feat. The former Warlord could effortlessly withstand the extreme temperatures of Levels 3 (where the heat is sufficient to roast a bird alive), 4 (which is several times hotter than Level 3) and 5 (a room operating at sub-zero temperatures) of Impel Down.
Crocodile also possesses great physical strength, first demonstrated when he carried off the dead bodies of an entire pirate crew (namely Puppu's) after dehydrating them with his Devil Fruit powers. While Luffy was unable to retaliate against Mihawk and was forced to only avoid his attacks, Crocodile intercepted and stopped Mihawk's two-handed slash with just his hook; he didn't seem to be worried at all about facing such a strong opponent, and even talked down to him. He also seemed to be able to fight Doflamingo, a pirate noted for his outstanding physical feats, as an equal: their clash creating a shock wave strong enough to push nearby Marines away.
Crocodile is extremely intelligent and cunning, which is apparent from his ability to lead Baroque Works while keeping the World Government completely in the dark about what he was doing and making himself out to be a hero in the eyes of the people. He is also skilled at crafting near-flawless plans and noticing things that most other people would not.
He is known to deduce a correct conclusion based on very little information; for example, after seeing the white wrappings on the Straw Hats' arms, he almost instantly figured out that it was a safeguard against Mr. 2's infiltration. He managed to sabotage the king's reputation among the citizens by secretly importing rain-producing dust into the capital during a period of major regional drought, then having it "accidentally" discovered en route, inciting the threat of civil war and thereby drawing attention away from his own shady machinations.
The entire Arabasta Saga is a testament to Crocodile's strategy and manipulative skills: he managed to successfully maintain control over all operations within "Baroque Works" over a period of years while keeping his true identity as a Warlord hidden from everyone except Nico Robin. Simultaneously, he strove to attain a high level of respect and prestige among the citizens of Arabasta as their "savior" by brutally dispatching any would-be invaders or pirates. An expert liar and manipulator, he was able to trick Vivi in wasting time looking for a key that was fake all along and managed to make Luffy drop his guard by targeting Yuba with a sandstorm, after learning of Luffy's friendship with Toto. During the events of Operation Utopia, Crocodile demonstrated great foresight in his attempt to blow up Alubarna, having installed a backup mechanism to fire a bomb on the capital in case the main method failed and placing two of hisagents to protect it in the possibility it was found.
In addition, aside from being heavily experienced thanks to his many years as a pirate, he seems to have a better understanding of Devil Fruits than most people, as evidenced by his mastery of his Logia-type powers. He also revealed that the Jailer Beasts were actually "Awakened" Zoan fruit users at a time when no one around him had even realized that they were even Devil Fruit users.
Crocodile ate the Suna Suna no Mi, a Logia-type Devil Fruit that allows him to create, control, and transform his body into sand. He has mastered his ability to the point of perfection and can turn into sand reflexively if attacked; this became especially obvious after Doflamingo cut his head off while he was distracted.
While in a desert area, his powers make him nearly invincible. Crocodile has the ability to create huge sandstorms, make multiple bladed weapons out of sand, and create quicksand (given the presence of a nearby underground waterway). He can also create powerful sandstorms that grow in power until even Crocodile himself cannot stop them.
He can absorb all the moisture out of any object, living or non-living, by touching it with his right hand. This ability allows him to utterly destroy his surroundings, killing and mummifying any biological substances via dehydration. This application doesn’t work on metallic substances though.
In addition to being one of the few characters shown to have some degree of mastery over their Devil Fruit, Crocodile is also formidable in hand-to-hand combat using a hook. He fought using only his hook for most of his third match with Luffy, only resorting to his Devil Fruit powers when he finally accepted that things weren't going in his favor. His hook is made mostly out of an extremely tough and resilient gold alloy, which makes it resistant to corrosion. Its durability was shown to be especially impressive when it took no visible damage from Mihawk's Yoru as Crocodile defended Luffy from an attack.
The gold part of the hook is hollow and can be removed to expose a poisonous hook hidden inside. This porous secondary hook releases a powerful scorpion venom, which is strong enough to melt through rock and kill anyone with the effect of a single slash.
In the unlikely event that the hook becomes damaged, there is a knife hidden underneath that can be ejected and used in its place. In a pinch, the very wide base of the hook can also serve as an improvised mace-like weapon, as shown when Crocodile used its blunt force to smash Luffy into a wall.
During his incarceration in both a regular prison and Impel Down, Crocodile was permitted to keep his formidable hook.
The golden hook.
The poisonous hook underneath.
The knife underneath the poisonous hook.
For the pinnacle of Operation Utopia, Crocodile prepared a specialized bomb. It was designed to detonate across a maximum radius of five kilometers, large enough to completely obliterate the capital city of Alubarna. It was prepared about 30 minutes prior to the intended firing time, at which point it would be released from a bulky cannon, but in case that method backfired, Crocodile had a special timer installed onto the bomb itself. The timer was set for less than a minute after the planned time.