In the first episode of Kidou Tenshi Angelic Layer, Misaki watches a match between two "Angels", although she didn't know what they were at that time. When it looked like the smaller of the competitors (Athena) was about to lose, she undergoes this state, thinking how people of her own stature could never go far, but breaks from it when Athena wins the battle.
The new manga of The Movie of Magical Girl Lyrical Nanoha explores this. Titular character is loved, has a family, has friends; she smiles for all of them...but something's....wrong.
In the first season, Yuuno talks about how he grew up without parents, being raising communally by his clan. In the drama CDs, he mentions the Scyra family tent, which was often full of a lively, bustling crowd of people, and how comforting he finds such an atmosphere. He tells Nanoha that he's always been alone in the crowd, but he appreciates what they did for him, and he's happy to bear the name "Scrya".
Except in this case it's a bit of a subversion, considering that he's walking through the crowd because his mission is over and the world is now a place where he can live like anyone else
95% of the opening theme of Monster is Tenma doing this.
In Monster Rancher, Genki has a nightmare about this early on, dreaming about being dumped back in the boring real world without Holly, Mocchi, and all the friends he made in the monster world. This turns out to be Foreshadowing for his actual return at the end of the second season, which is jarringly traumatic.
Played with in the opening to the first Hell Girl season. Near the end of it, we see a greyed-out, bustling crowd, with the Hell Girl herself in the middle of the crush, staring in full colour at the camera. Possibly used in this case to highlight that Ai is not part of this world, and as such literally alone in the crowd.
The day after Mami's death in Puella Magi Madoka Magica, Madoka feels like she's in a foreign country, surrounded by strangers. Sayaka agrees, and explains that it's because no one else knows what happened. The visual version of the trope is used a few times, such as at Sayaka's funeral.
The final shot of Fritz Lang film Scarlet Street shows Chris, who has gotten away with murder but is now homeless and wracked with guilt, shuffling down a crowded city sidewalk. Then the other people fade away, and Chris is shuffling down the street alone.
In Cavalcade, the main character finds out that her son has been killed in World War I just as the bells toll announcing the armistice that ended the war. She staggers out of her house and wanders through the joyful crowds, dazed with grief.
The central theme of 1928 silent classic The Crowd, in which the protagonist discovers how indifferent The Crowd is when his life falls apart.
In Accepted, this happens to Bartleby Gaines. He is visiting Harmon College to get an idea of how college works. He quickly becomes jaded by the students, who are either apathetic or stressed out. He freezes in the middle of the frame as a speeded-up crowd rushes around him.
In Iron Man 1, Tony Stark does this when he finds out Obadiah Stane tried to get him fired from the company board.
Bruce Willis does it in Unbreakable — slight variation in that he's deliberately expecting people to bump into him in order to trigger his newly discovered Detect Evil power.
John Preston in Equilibrium. Probably many of the sense offenders as well, but the movie doesn't focus on them.
In the Ian McKellen film version of Richard III, before the "Now is the winter of our discontent" speech Richard moves through a party but stays isolated from the celebrating nobles.
In Titanic, right before Rose attempts suicide, she's sitting at the table in the lobby, narrating, but her body doesn't move. This is less to do with a shocking revelation, and more to do with her feeling that if she screamed, no one would hear, or even care.
The protagonist in The Tiger Makes Out, a disgruntled postal worker who sees himself as an intellectual in a world of sheep, walks the streets of New York angrily talking to himself while people stream around him at double speed (done by speeding up footage of him walking at half-speed.)
Taxi Driver - "Loneliness has followed me my whole life, everywhere. In bars, and cars, sidewalks, stores, everywhere. There's no escape. I'm god's lonely man."
Conan the Barbarian - In Robert E. Howard's Beyond the Black River, the presence of Conan does not keep Balthus from feeling alone in the wilderness, because Conan is native to the wild. Unusual in that Conan is the only person there, but he actively reflects on how the other person does not keep him from feeling alone.
In A Game of Thrones, Tyrion's isolation because of his dwarfism is emphasized as he walks through his father's war camp:
The Lannister camp sprawled for miles between the river and the kingsroad. In amongst the men and the horses and the trees, it was easy to get lost, and Tyrion did. He passed a dozen great pavilions and a hundred cookfires [...] No one looked at him. No one spoke to him. No one paid him any mind. He was surrounded by men sworn to House Lannister, a vast host twenty thousand strong, and yet he was alone.
The second Alex Rider book reintroduces us to the main character with this trope.
In The Return, one of the last books in the Animorphs series, Rachel at one point walks through the hallway of her school - a setting that has not been featured in several books as the war has taken an increasingly grim turn - and reflects that she no longer feels like she belongs there at all and can't even pretend to anymore. Sure enough, she has a breakdown in class a chapter later and flees the school. This is the last time school is visited, as in the next book the Animorphs all become fugitives and have to go into hiding.
This trope is almost synonymous to Mika Waltari's stories, but most prevalent in The Egyptian and The Wanderer.
Played out literally in Fritz Leiber's "You're All Alone" where the awakened, such as the protagonist, are surrounded by people acting out the automaton of everyday life life while the awakened find themselves getting more and more out of synch with the script as time passes.
In Smallville, Clark is this when he sees Lana and Lex hugging.
The Shokojo Sera episode "A Sad Farewell" is a good example - after leaving the Seminary, Sara walks around the streets of London in a daze.
In the first episode of Scrubs, J.D. struggles to cope with his first day as a doctor, rubbing his temples while blurred, fast-motion people swarm around him. Happens again in "My TCW", J.D. wanders despondently down a hallway surrounded by busy hospital staff as he narrates how it's important to hold on to the relationships you have and laments how awful it feels to be alone - and providing the page quote.
In the pilot of Veronica Mars, Veronica sits at the lunch table, reading a book, as the entire student body moves around her in fast-forward. This isn't exactly the same, however, as Veronica has already been jaded by the death of her best friend, disgrace of her father, and her own date-rape, she has simply accepted her status as a loner. And then the new kid sits down beside her...
In the NCIS season 7 premiere, after Tony believes that Ziva is dead, he is shown at his desk just sitting there in shock, the rest of the world whirling at a fast pace around him.
Happens in the AMC series Rubicon, in the first episode. The protagonist is in a diner and sees on the TV that the train his father-in-law was on was involved in a deadly crash. He then walks out onto the street in a daze, amidst a crowd of people.
Doctor Who, during episode "The End of the World", has the Ninth Doctor return to modern-day Earth and stand in a crowd of bustling city folk, lamenting the destruction of Gallifrey at the end of the Time War. Averted in that the Doctor is not alone: Rose is right there to comfort him.
You Are Beautiful: Mi Nam and Shin Wo just miss each other in a crowded marketplace, even though they are standing mere meters apart.
The 1980's Twilight Zone revival, episode called "To See the Invisible Man". The protagonist is sentenced to be "invisible" for a year (really just aggressively ignored by everyone), and so spends most of the episode with people moving around him as if he wasn't there.
Homeland literalises the trope to chilling effect during an episode in series 1, when Dana Brody fast-forwards a video she took of her father during a visit to Gettysburg — and shows him standing completely still as the crowd blurs around him.
Summed up in Spamalot with the song "I'm All Alone".
The Good Ending of inFAMOUS has it to where Cole after his best friend Zeke betrayed him, his girlfriend was murdered, and it turned out that this was all orchestrated by himself from the future, he states how he couldn't feel more alone.
The World Ends with You - Despite the Reaper's Game taking place in the oh-so-crowded district of Shibuya, the players of the game are alone in the crowd— non-players can't see them, can't hear them, and definitely can't help them.
The animated intro for Hanako's route in Katawa Shoujo has her standing alone in a fast-forwarded crowd. And then, subverted: she notices Hisao is also there, and the rest of the crowd vanishes as they walk towards each other.
In the second game of Jack French, the protagonist is briefly shown standing at an intersection while people whiz around him after the car crash that kills Elizabeth.
While not seen, he also goes by himself to amusement parks and eats alone at Chuck E Cheese's, just to blend in with everyone else.
The SCP Foundation gives us SCP-451 quite possibly the most literal and horrific form of this trope: A man who, thanks to exposure to an artifact, is unable to perceive or interact with the people around him in any way.
Andrew Stanton stated that in WALL•E, a major theme was the contrast between WALL-E's isolation in the first part of the film to the presence of this trope on board the Axiom.
Referenced verbatim in the obscure cartoon Captain Star. "Limbs" Jones, who has nine heads with independent personalities, is upset because he is alone. The Captain points out that he has nine heads, and Scarlet replies "One can get lonely in a crowd".
Sometimes people with depression or another milder mental illness can look at a huge group of people and say "I'm not one of them", because they truly feel like they don't belong.
Scratch that, make that anyone who's ever been lonely.
In other words, everyone.
This photo of UK Labour Party Leader and prime ministerial candidate Ed Miliband.