Be warned, this series is over 10 years old with over 700 chapters to its name.Spoilers may not be covered below.Tropes pertaining to the entire crew
Always Save the Girl: The crew goes before everything else. That level of devotion is where the Protagonist-Centered Morality comes from, as while the Straw Hats are genuinely good people, they tend to prioritize each other and their friends before everything else.
Animal Motifs: They all have them. According to Oda, they are as follows: Monkey for Luffy, Shark for Zoro, Cat for Nami, Duck for Sanji, Armadillo for Usopp, Reindeer for Chopper, Crane for Robin, Bull for Franky and Horse for Brook. And for the ships, it's Sheep for the Going Merry and Lion for the Thousand Sunny.
They don't really care about politics, and as a rule have a "live and let live" attitude when it comes to the oppressive customs of countries they visit. Barbaric cruelty towards the helpless and/or innocent WILL rouse their anger, but in general they only fight tyrants when It's Personal.
That being said, due their friendliness and generally good nature, they tend to make friends wherever they go. As a result, they almost always inevitably come in conflict with oppressive regimes harming their new allies. When they topple said regime to save them, they earn the friendship of all the inhabitants of islands they liberated.
They are one of, if not THE most eccentric crews on the Grand Line. They are also one of the most powerful and legendary ones as well, having defied the World Government several times and have practically gotten away with it. They've broken into one of the most secure government facilities in the world, while Luffy, The Captain, has also broken into the other two. One of them, he broke into twice.
To clarify: The crew wages war on the World Government's courthouse and makes a mess of it, later nullified by the Buster Call out right destroying the whole island bringing down thousands of armed guards and the World Government's best assassins in the process. Then Luffy breaks into Impel Down, an underwater prison/fortress/hell and then breaks out with 240 other prisoners (only one other pirate had ever gotten out ever), and then arrives at the Marine Headquarters in the middle of a war with said escapees. By falling out of the sky in a battleship. A few days later he strolls back into the Headquarters, makes a statement by ringing a bell and having a moment of silence and then walks out.
They've also defeated two of the Seven Warlords of the Sea, a Carnival of Killers who are some of the biggest badasses in the setting.
Break the Cutie: All of their backstories have shades of this, to varying degrees.
Bully Hunter: Not intentionally, but as of the Sabaody Archipelago Saga, the Straw Hats have become feared amongst tyrants and despots for being this trope.
Bunny-Ears Lawyer: They're an utterly random collection of individuals, quirky as hell (even the relatively saner ones), and about as far from normal pirates in this series as one can get. Get on their bad side, though, and they'll show you just how they earned those seemingly ridiculous bounties.
Cloudcuckoolander: Every single one of them, to varying degrees. Even Nami and Usopp, by far the most grounded members of the crew, have their moments: Nami's reasoning flies straight out the window and plunges down into the sea the very moment money is mentioned, while Usopp is a perpetual liar whose fear often gets the best of him, and frequently joins in on Luffy's antics. Sanity is in no way a priority with this crew...
Cloudcuckoolander's Minder: ...but Luffy's head is so up in the clouds that everyone, including a similarly crazy Zoro, function as this for him.
Dark and Troubled Past: ALL of the crew members have a painful past that makes you wanna give them a hug, especially Robin, Nami, Brook, and Luffy.
The Dreaded: Following the timeskip, the crew has such an infamous reputation that only veteran New World pirates or vice-admiral class (or higher) fighters would dare to get on their bad side.
Dysfunction Junction: With the exception of Luffy at first, all of them have complicated quirks that somehow mesh together in a weird family bond unlike any other crew in the series.
Famed In-Story: In the beginning they're nobodies who get laughed at wherever they go. By the Time Skip they're considered one of the most dangerous pirate crews in the setting and are always instantly recognized.
Fire-Forged Friends: Really becomes evident during the climax of the Arlong arc, and reinforced during the Enies Lobby arc.
Friend to All Children: The Straw Hats act as big brother/big sister figure towards the children they meet in their journey. Which means they don't take it very well when the Big Bad hurts one.
From Nobody to Nightmare: To the world's eyes, Luffy started off as an overly-ambitious kid. Two years and a whole lot of adventures later, his crew is considered legendary, and the manga isn't even over yet!
Heroic Neutral: They're pirates who do not commit acts of piracy. All around, they're the nicest crew in the series. When you closely examine their heroics though, you'll notice they very rarely go after any of the antagonists until one of their own gets targeted. This extends to people they consider allies as well.
Hidden Depths: Whether indicated in backstories or present events in the story, none of them are exactly what they seem at the surface.
Hypercompetent Sidekick: Everyone is this to Luffy. Unless it's fighting, eating, or personal/friendship related, Luffy sucks at it. Luffy himself has acknowledged this.
The Idealist: A whole crew of them, unified by their unwavering desire to achieve their collective dreams.
Improbable Age: The crew as a whole qualifies, considering how powerful and well-known they are. Most of the crew are teenagers or young adults, and even the oldest members of the crew are fairly young (even Brook, who is 90 post-timeskip, died at age 38, which isn't terribly old).
Jack of All Stats: As a whole, they are not physically stronger, faster, or smarter than other crews or the Marines. However, with each crew member falling under some varying niche, it allows them to exploit a weakness their opponents have, or one crewman cover the others when their weakness is exploited. For instance, when faced against Perona on Thriller Bark, only Usopp could stand against her as he was such a pessimist, her pessimist-causing ghosts became depressed by touching him.
Parental Abandonment: Most all of them had adoptive families; Usopp's the only member so far who's even shown to have both biological parents, and even then, when he was a kid his father left and never came back, and soon after his mother died of an illness.
Party Scattering: At the end of the Sabaody Archipelago arc, courtesy of Bartholomew Kuma. They get back together after the Time Skip.
The Pirates Who Don't Do Anything: Their only legitimate act of theft was to steal some gold from the Shandorians... who would have given them far more if they hadn't run away!
The Power of Friendship: The mere hint that one of their companions is troubled or in danger by an outside force will make them rise up to defend the friend. Even making them withstand what should be normally fatal attacks or situations simply because their friends need them.
The Power of Love: Many of Luffy's actions are driven out of the intense love he has for his crew — there is nothing in the world Luffy wouldn't do for them. They in turn are willing to do almost anything for him, putting up with his selfishness without a second thought.
Ragtag Bunch of Misfits: The crew consists of a rubber man, a swordsman, a thief and meteorologist, a cowardly sniper, a kick-boxing chef, a shape-shifting reindeer doctor, an archeologist, a soda-run cyborg, and a living skeleton.
Red Baron: All members have one, to go along with their badassery. The only one whose nickname isn't badass is Chopper, whose cute appearance led the Marines to believe he's the crew's pet.
Sir Swears-a-Lot: The entire male crew's mouths could use a serious scrubbing with industrial-strength disinfectant; somewhat justified in that they do literally "swear like sailors." The Taiwanese translation of the manga in particular give them vocabulary so foul and vulgar it would make Eminem himself blush in embarrassment.
Nami can be almost as rough as the guys, though she is not very fond of Toilet Humor and thus usually avoids words like "shit". She can be more than the guys in certain translations (like in the Danish and German ones), probably to compliment her Pirate Girl image.
Spanner in the Works: This crew is the main reason why several villainous plots on the Grand Line haven't succeeded. It's either because they befriended someone who just happened to be directly affected by said plot, or thwarted said plot unknowingly while trying to accomplish a completely different goal.
Took a Level in Badass: They start out well enough with Luffy, Nami, and Zoro. But with each arc finished, they Level Grind to a stronger point of Badass and gain a new member, each one even more awesome than the last. Then there was their jump after the time skip, to the point a previous hurdle was taken out with a basic attack.
Underestimating Badassery: Can go both ways with this crew. On the one hand, they'll happily jump to meet the next challenge, regardless of the danger posed (in fact, Luffy would have it no other way). On the other, their enemies are equally caught off guard by just how much trouble this crew can make when they set their minds to it, as lampshaded by Trafalgar Law.
Undying Loyalty: No matter whatever hardships they face, no matter the burdens they carry, not a single member of this crew will ever betray Luffy. Ever. Likewise, this crew is the main reason why Luffy bothers continuing to live.
Unwitting Pawn: Possibly to Trafalgar Law, depending on what exactly his true intentions are.
Turns out they're more of Spanners In The Works since Law's plan isn't going as smoothly as he liked. For one, the captain felt the need to not follow it through because he got too pissed off with the target, and sent him flying.
Mentioned by Law himself. When Smoker confronts him about this after the battle at Punk Hazard is over, Law mentions he is not so sure who is using who. He is referring to Luffy's plan of fighting all of the Four Emperors. This makes sense as before we found out it was Kaidou, Luffy had plans to fight 3 out of the 4. Shanks because of their promise, Blackbeard for retribution and Big Mom to free Fishman Island. With Kaido being targeted by Law, this alliance serves Luffy's purposes to take down all of them, as long as Shanks is last.
It became evident in Chapter 700 that Law, despite being the one who's calling the shots on the plan they have to take down Kaido, is not the one in control, and probably never was in the first place. He's eventually going to realize that Luffy does what he wants and does not give a damn about the consequences. Then he'll realize that he's being sucked into Luffy's circle, just like Luffy's entire crew did when each of them first met him.
Vitriolic Best Buds: Read any chapter and you're likely to find one of them yelling at another one (Sanji and Zoro, though, take the cake on this one). Don't ever let that fool you, though, they're as close as family.
Weirdness Magnet: It's deliberate. Most pirate crews on the Grand Line carefully calculate their routes to avoid danger. This crew on the other hand goes on the most dangerous route possible for the captain's amusement.
It gets worse in the New World. The Log Pose there has three needles, and the ones that shake the most violently are the most dangerous. Nami has a major freak out about the possibility of Luffy finding out (which he does, mere moments later).
Wild Card: There exists a tentative stability between the pirates and the Marines, which most crews can be expected to abide by. The Straw Hats are not one of those crews.
Worth Living For: This crew is filled with misfits and (in society's eyes) freaks. There isn't much that many of them have to live for — but for many of them, this crew, their family, is enough.
After Ace's death, Luffy was close to crossing the Despair Event Horizon. Yet in the face of such an overwhelming tragedy, it is ultimately his crew that gives him the strength to move on and live his life, as Ace would've wanted him to.
Would Hit a Girl/Wouldn't Hit a Girl: The male members of the crew, or more specifically, the Monster Trio, having this in descending order. Luffy would hit a girl because it really doesn't matter who or what you are; if you piss him off, he will hurt you. Zoro will fight women, but he has a tendency to use the bare minimum of force it takes to defeat them. Sanji, however, will never hit a woman. It's not so much the belief that they're weak than it is his upbringing that prevents him from doing so. Though it doesn't stop him from bluffing, like he did with Robin back before she joined the crew.