For new readers, they must get educated as to what a CLAMP book is like (since there are many CLAMP series and it's better to found out earlier that you're a fan than later). I suggest "Chobits" is a good starting point. From there, decide if you like apocalyptic manga, or light and cute manga because CLAMP's got a lot of both. For apocalyptic manga, choose X/1999 (before it goes out of print), and for light and cute, choose Wish and Cardcaptor Sakura.
I agree completely that being educated on CLAMP is important. CLAMP, a group of four manga-ka, is popular and have been in the biz for 20 or so years. Now, there is a reason I didn't suggest any CLAMP titles in the first post: CLAMP is evil and quite possibly insane. Expect homoeroticism, eye gouging, and horrible things happening to good people. On the other hand, one of my first titles was by CLAMP. It was, of course, Cardcaptor Sakura, made available by Tokyopop through their now defunct Chix Comics imprint.
The series is twelve volumes long; the second six volumes are titled Cardcaptor Sakura: Master of the Clow in the English release. (I've been sticking to things I know are available in English.) Adorable Kinimoto Sakura must capture the Clow cards, a plot anyone with the slightest familiarity with anime can recognize. Of course, in most of those stories the main character and her love interest don't have a rivalry over the affections of another guy. Oh, CLAMP. Of course, while this story has the tangled webs of love and gets progressively darker, it's still basically a fluff series that has nothing on CLAMP's darkest moments. In addition, there's no eye-gouging.
For those interested in the anime, find a subtitled version. The English dub chopped it up, changed the episode order, and generally sucked.
Chobits is a shonen series, heavy on the philosophy and slight on the SF (despite featuring an android) . . . and also heavy on the adult humor. But hey, I read it in middle school.
Filled with adorable loli-style art and adorable moments of unbearable cuteness between the pervy stuff, I love CHOBITS. It's a well-plotted series that sets up and establishes a relationship in seven volumes even with all kinds of crazy conspiracies going on. The fanservice does decline toward the end, as the characters try to discover whether a human and a persecom can truly love each other. It's classic CLAMP and yet half as crazy as their usual fare. (No eye gouging, for one.) I adore the anime, despite the filler episode about shopping for underwear, if only because it has a fabulous opening theme.
For the final one Oliver suggested that I've read, is one of my favorites: X/1999.
Okay, the art is a little dated and people tend to look like triangles (broad shoulders, tiny waist). The sound effects in English are ridiculous. Until you reach far enough in the series to learn the characters' motives almost all of them seem like unsympathetic jerks. That is, except for poor, doomed Kotori, who just wanted to become an indigo dye expert. Anyway, what happens when you throw together Buddhist, Shinto, and various other mythologies with stylistic use of Christian symbolism to depict the battle over the fate of the world? Pure, crazy awesome. There's a schoolgirl in love with a middle-aged man that's possibly the sweetest romance in the entire thing. And yes, there is eye gouging. Romantically significant eye gouging, at that.
The series went on hiatus (at eighteen volumes, at a CLIFFHANGER, basically) after 9/11, as the violence and wanton destruction of major landmarks kept increasing and CLAMP refused to censor themselves. However, two endings are available in the anime (simply known as X - X/1999 is an English-only title) and the OVA (ie, movie). The movie just makes everything 30x more incomprehensible. The TV series is pretty good and even manages to make the characters more sympathetic. Episode 9, which introduces Subaru, is a work of art. It's even more beautiful if you understand the Buddhist symbolism, but it's incredible without it.
Of course, to get the lowdown of the relationship between the characters of Subaru and Seishirou, you have to read Tokyo Babylon.
This is the story of a Bet. It's also the story of a 25-year-old veternarian romancing a 16-year-old boy while the boy's twin eggs it on. It begins fairly episodic, with Subaru going about various onmiyoji jobs. (An onmiyoji is something like a medium/exorcist . . . in short, he's got awesome supernatural powers.) Now this one starts rather adorably but slowly crumbles that veneer until the tragic ending. It's seven volumes of superb storytelling. This one contains eye gouging.
The OVA is only two episodes long and skippable.
Another series that gives some background for X/1999 is Clamp School Detectives, which I have not read. (I'm fairly sure there is not eye gouging.) It was adapted into an anime that fans generally hate.
To continue the steam of interconnected series, I'll next talk about CLAMP's two current projects.
First is xxxHolic.
CLAMP's artwork started out lovely, but I think this series features the most beautiful art. Watanuki can see ghosts and can only not see them in the company of Domeki, the rival for his crush's affections. Pretty soon he's indebted to the Time Witch . . . and things just keep getting worse for him. This one also starts off episodic with "be careful what you wish for" type parables. Then the overarching plot begins to become evident, although it might make no sense if you don't read TSUBASA as well. If you do read TSUBASA, the plot makes sense if you make an effort not to think about it. Eye gouging that's practically Disney by CLAMP's standards.
The anime is a decent adaptation, but due to copyright issues avoids referencing TSUBASA. This might make trouble as it continues and the plotlines become increasingly interwoven.
This brings be to Tsubasa: RESERvoir CHRoNiCLE, the epitome of begin fluffy and become completely dark.
Knowledge of Cardcaptor Sakura will aid in reading this one, as will knowledge of xxxHolic. Alternate-universe versions of characters from all of their other series will make appearances, but they're more like bonuses if you recognize the series. Sakura loses her memory and falls into a coma and her childhood friend Syaoran wants to save her. The price? Her memories of their relationship. Soon Syaoran is on a roadtrip through universes with warrior Kurogane, magician Fai, and Mokona. Then the Acid Tokyo arc happens. CLAMP has never had this much fun with eye gouging before. And as those of you who read the scantilations before the official translations, it just gets weirder and weirder. I'm pretty sure they've violated their own canon. Also, the art is purposefully a little rough and generally excellent, though action scenes can be a little hard to follow.
The anime started speculating too much during the filler, so CLAMP back their rights (or whatever) and a new adaptation will be out soon.
One of their titles that might be good for a beginning reader is Magic Knight Rayearth.
This one combines schoolgirls falling into another universe, Magical Girls, and mecha. The first series plays fairly straight with the typical trappings of those genres, but the second series explores the consequences of their actions. Generally a very good series that is much more straightforward than most of what CLAMP does. It's been awhile since I've read it, but I don't remember eye gouging. The TV series (two seasons) changes some elements from the manga, leading to plot holes. The three episode OVA barely resembles the source.
There are only two more CLAMP series which I've read. The first is the three volume Legal Drug, which is currently on hiatus.
Rikuo discovers Kazahaya passed out in the snow and takes him to the shop where he lives and works. Soon the two are running odd errands together. It's an interesting series with fabulous art, but I don't recommending getting into it since it currently stops just as the plot is picking up speed. However, anyone who can explain to me what the marijuana leaf motif has to do with anything gets a cookie. No eye gouging. Yet.
The 10-volume RG Veda draws heavily on Buddhist and Hindu myth.
It's pretty, but it is an early work and CLAMP didn't quite have the chops to pull the complicated story off. It's still good reading and features a number of sympathetic, complex characters. I don't recommend it for manga beginners. At this point CLAMP had yet to develop a penchant for eye gouging. There's an OVA that doesn't fit into the storyline.
Other CLAMP works currently available in English include Angelic Layer, Legend of Chun Hyang, Miyuki-Chan in Wonderland, Suki: A Like Story, and Wish. Clover is out-of-print, but it's rumored Tokyopop will print a new edition soon. Let's keep our fingers crossed, because what I've read of it was minimalist and beautiful.