Clone Troopers are, as their name implies, the predecessors of the stormtroopers.
The vast majority of the Clone Army was born on Kamino (save for the 1337 men of the 501st and the Shocktroopers, but we'll go into those guys later), and a precedent was immediately by setting aside no less than three batches of troopers for special operations activities, while the rest of the poor sods were sent over to the regular infantry.
Standard infantry clones were trained by using something called a learning helmet, which was pretty much a cross between VR and the Internet on steroids.
"Whoa...hey, Two-Niner, there are females that aren't Kaminoans!"
The commando batches had to deal with this as well, but they also had the added benefit of being trained by the space marine equivalents of R Lee Ermey. Standard operating procedures for these training sergeants included mercilessly beating the living hell out of the clones, act in as condescending a fashion as humanly possible, and brainwashing the shit out of these guys with whatever culture you happened to come from.
"I see no problem with that."
Whether commando or infantry, all troopers took part in live-fire exercises, and not all of them made it out. Whether this was due to being shot or just being fragged for whining too much (a sadly common situation amongst the commando batches) is up for debate.
The 501st Legion
Kicking ass and taking names since Geonosis.
Ignore the somewhat ridiculous looking armor scheme; you did not want to mess with these guys. The 501st wasn't founded as such until midway into the Clone Wars, when Palpatine, presumably evilly sipping some tea while surveying unit battle records, had an epiphany. This epiphany was simple: such amazingly badass soldiers could be used to train his own super-secret-elite unit. So some of the best clone troopers were yanked from their units and sent to Coruscant, where they trained the first clones grown off of Kamino, who soon became the 501st Legion.
During the Clone Wars, these guys were Anakin Skywalker's shadow, and when Order 66 went down, they were sufficiently badass to handle the assault on the Jedi Temple. The badass factor of the 501st was further enhanced following the transition to the Stormtrooper Corps, during which they went from being Anakin Skywalker's personal unit, but Darth freaking Vader's. Hell, the good Darth was so proud of them that when a Jedi killed their commander, he actually eulogized the guy. If that doesn't increase your badass factor, nothing will.
The 327th Star Corps
Make fun of our skirts. We dare you.
These yellow-striped guys knocked about the galaxy during the Clone Wars, never returning back to Coruscant. They were basically the Texas Rangers of the GAR: when there was a droid attack, the Star Corps would be there to stop them. But that's not why we remember them.
This Gossam knows why we remember them.
Yes, the 327th had the distinction of having pretty much the hottest General in the GAR, the Twi'lek Aayla Secura. Corps-wide, Clones who hadn't heard of the word puberty, let alone comprehended it if they had, suddenly had first-hand access to one of its effects during their long campaigns. If you don't believe me, take a look at the duel between Aayla and one Aurra Sing that some Corps members happened to witness.
I rest my case.
The best part of it all? Aayla was the kind of General who took care of the needs of her men, if you get my drift. For those of you who don't, I'll just let Jedi Master Arligan Zey say it: "General Secura is getting a little too close to Commander Bly, and while I applaud the dedication to the men under her command, this can only end in tears."
Sadly, he wasn't wrong.
The 212th Attack Battalion
Now it's a party!
Under the charge of Commander Cody and Obi-Wan Kenobi, these guys compensated for having a somewhat lame paint scheme by kicking extreme amounts of droid ass. Wherever Skywalker and the 501st could be found, chances were Kenobi and the 212th would be in the thick of the action as well. Heck, these guys even saved some of the 501st once, during Teth.
Save those blue-painted pansies? Right away, Sir!
Cody and his boys were also the first clone units sent to retake the planet Ryloth, presumably in hopes of being thanked by a horde of Aayla Secura lookalikes.
They were sadly disappointed.
The 41st Elite Corps
"Come on, you pansies, load it up. The Corps ain't payin' us by the hours. Or at all..."
You know those guys in 'Nam whose job it was to basically go behind enemy lines and establish a rapport with the locals while blowing shit up at the same time? The Clone equivalent of that was the 41st Elite Corps. They were also noteworthy for being the only guys in the GAR to actually use camoflauge.
"Haha, can't see me now, can ya clankers..."
The 41st Elite was under the charge of Commander Gree, who was basically that one guy in your History class who makes a joke about some obscure Nazi general and then is insulted when nobody laughs. Only instead of joking about Nazi generals, Gree was into aliens. Not like that, get your mind out of the gutter, he was just into learning about obscure alien cultures.
"Nice...head-tails, General Secura."
The 41st Elite were were typically to be deployed on "unconventional warfare" missions, long patrols behind enemy lines, forging alliances with natives. In theory. In practice, however, they often found themselves getting the shit shot out of them as standard infantry, on worlds from Dinlo to Geonosis Round Two to Kashyyyk. This last deployment would not be a happy memory for the 41st.
"Fuck you, Yoda."
What do you get when you clone one of the most badass men in the galaxy one hundred times, without making any modifications whatsoever to ensure the obedience? The most badass soldiers in the galaxy. So badass were the ARCs that it took the invasion of Kamino to persuade the Kaminoans to activate them. The ARC troopers specialized in infiltrating enemy lines, taking out strategic targets, and generally kicking some serious droid ass.
Not an official GAR unit, this special operations unit under former training sergeant Kal Skirata consisted of two clone commando squads, a bunch of batshit insane ARC trooper variants, and far more Mandalorians in one place that is good for anyone's sanity. Specialties of the team included whining, seducing Jedi (both sexually and into joining the freakin Mandos), and generally ignoring the very chain of command and government that the Clone Troopers were created to protect. These guys---the majority at least---wound up deserting at the end of the Clone Wars.
"I see no problem with that."
Whether or not these deserters will be curb-stomped by the Empire---the most likely outcome of such treason---remains to be seen.
When the existence of the Clones was first revealed, everyone considered them to be extremely badass guys, if not exactly humans.
Then this guy came along.
This guy is an ARC trooper by the name of Alpha, and he was pretty much the first clone trooper to be treated as a character and not a redshirt in white armor (pauldron color not withstanding). Alpha took no shit from anyone, and even mouthed off to Anakin Skywalker at one time. After several arcs of ass-kicking in Dark Horse's Republic comic series, Alpha was sent back to Kamino to train Clone Commanders in his ways of badassery. The first clone character was pretty much put on a bus.
But by that time, many other authors had jumped on the "clones are people too" bandwagon, with results that ranged from mediocre...
To freaking amazing...
To still great...
To a shocking swerve by that same author into the depths of Clone emo-dom that also happened to feature obnoxiously bad cover art.
We're looking at you.
To top it all off, these writers committed the unforgivable sin of not specifying the numbers of troopers in the GAR, which to you and me might seem ridiculous, but to denizens of the internet is madness.
So a woman by the name of Karen Traviss, who with her book Hard Contact (which was not, surprisingly, a detailed account of how the troopers dealt with sexual frustration) had become the pre-eminent clone author, was assigned to write an article for Star Wars Insider magazine, called the Guide to the Grand Army of the Republic, in which she would establish a solid organization for the Clone Army and maybe add in some fun facts to boot.
This picture sums up the internet-dwelling Star Wars fan's reaction:
Sadly, no Waahmbulance was on hand.
Apparently the numbers were off or something, nobody really knows, and the comments section of this article will likely become a battleground over this. What people do know is that Traviss's popularity took another downturn after the publication of her next Republic Commando book, Triple Zero, which featured copious amounts of Mandalorians, hot Clone-on-Jedi action, and generally far too much angst than is appropriate for what is supposed to be the most badass army in the history of the galaxy.
"I see no problem with that."