TV Tropes [WIP]
Canon
Ascend to a Higher Plane of Existence: Eiri's goal, Lain's eventual solution.
Blood-Splattered Innocents: Lain in her first Crowning Moment of Awesome against a drugged up clubber with a gun.
Cheshire Cat Grin: Lain's evil personality seems to wear one near-constantly. The Cheshire Cat itself is around, too.
Cooldown Hug: Lain to Alice in Layer 13. It does not quite fix her, but she does calm down.
End Of The World Special: Lain has one at the end of the series.
Evil Twin: The other Lain.
Fake Memories: Initially Lain, everyone by the end of the show.
Fetish Fuel: Lain is small, frail, quite pretty, a computer genius, has an affair with Alice and often goes barefoot, wearing a flimsy night-dress with the straps slipping off her shoulders (and no bra). Then there's the whole Split Personality thing, which lets you choose between the shy girl or the fierce one, and also allows for some Screw Yourself at some point... Canon also shows us she is capable of using the Wired for voyeurism purposes.
First Kiss: Taro gives Lain hers. It's kind of glossed over, though. She ends up with his chewing gum.
Hacker Cave: Lain turns her room into one. Her room is actually the trope page picture.
Heroic BSOD: Lain's sister Mika, after the 5th episode. Also Alice Her Heroic BSOD is what inspired Lain to Retcon herself out of existence.
Inside a Computer System: Pretty much the entire soul and fiber of the story!
I Want My Beloved to Be Happy: Only Lain takes a more... shall we say... 'active' role in Alice's life even after this...
Little Miss Almighty: Lain.
Mind Screw: The best way to describe Serial Experiments Lain is to throw paranoid schizophrenia and depression in a blender, along with a heavy dose of philosophy. After blending on the "puree" setting, add a dash of conspiracy theories and Accidental Nightmare Fuel, to taste.
Neuro Vault: Lain is an Artificial Human program created to hold the Version 7 network protocol within her brain.
No Social Skills: When we first meet Lain she has a wide-eyed befuddlement when faced with a social situation, to the point where she is almost mute. Her friends bubbly interchanges are juxtaposed with an odd - troubling gap where a response should be. She develops some skills as the series progresses: it is uphill work and Lain is never the normal girl.
Oracular Urchin: Lain.
Ordinary High School Student: Lain starts as one, grounding the series. She proceeds to become
somewhat less ordinary.
Parental Abandonment: Lain's parents turn out to be adoptive, because Lain is an Artificial Human.
Ret Gone The series ends with Lain doing this to herself.
Romantic Two Girl Friendship Lain's attitude toward Alice involves a romantic tint. It is open to interpretation how serious it is and whether Alice returns it.
Split Personality: Subverted by later making them split unpersonalities.
Technology Porn: Depending on who you ask, this is slightly more literal than in most cases.
Tomato in the Mirror: Lain herself.
Uncanny Valley Girl: Lain of course, seeing as she is very pretty, quiet, and seemingly normal at first, except she's not a normal girl.