X1999 also begins with a "prophetic dream"?really a few moments of the dreamer's next day at school.
Haibane Renmei starts with a dream the main character has immediately before hatching from her cocoon, and spends most of the first few episodes having the world of haibane explained to her, as she has no memory of who she is or where she's from.
Excel♥Saga episode 4, in its parody of Dating Sims, has this: Excel looms over the bed telling the player to wake up, or they will be Late for School. In the game, Il Palazzo kills Excel before even leaving the room because she lied to force him out of bed, earning a bad ending.
Project A-Ko starts with just this trope. Moreover, because she has superpowers, she does a lot of collateral damage rushing to school.
Neon Genesis Evangelion spoofs this in the final episode of the series. Shinji is shown a vision of an alternate life for himself, in which his life is more like a typical shounen series—including being woken up by Asuka, who is now his Unlucky Childhood Friend.
Come to that, this is exactly how the Angelic Days spin-off manga starts. Asuka is changed to Victorious Childhood Friend, however. (Which makes sense, as said manga takes place in the same alternate universe—which is explicitly stated to be a real alternate universe that exists somewhere in the canon multiverse.)
Princess Tutu opens with Ahiru having a nightmare and tumbling out of her bed.
Chrono Crusade starts this way as well, although with a bit of a twist. In the manga, Chrono is sleeping in a car when Rosette gets a call to go on a mission. When he's slow to get up, Rosette (literally) kicks him out of the car. In the anime, both Chrono and Rosette are asleep in their car when they get the call—Chrono wakes up first and gently wakes up Rosette, since he's worried Sister Kate won't want to speak to him.
Being There opens with Chance the gardener being awakened by his television set, and as the opening credits roll we watch him as he gets up, tends to the garden (where there is a TV in the greenhouse), watches TV back up in his bedroom, and then goes down and waits for breakfast, watching TV while he does so. As Chance is a middle-aged man, this also serves as a good introduction to exactly what kind of person he is. And then the plot kicks in when the maid tells him the master of the house is dead.
The introduction to 10-year old Harry Potter, in both the book and film version, involves him being woken up by his Aunt banging on the door of the cupboard he sleeps in, demanding he make breakfast for his cousin. Even before that, when we are first introduced to Harry, he is happily sleeping in Hagrid's arms, ending up woken by Aunt Petunia's shriek when she opened the door to put out the milk bottles.
The Death of the Vazir Mukhtar begins with the main character waking up in his family's house in Moscow, having arrived there from Persia the day before. He then goes on social calls.
Pokémon Live! begins with Ash sleeping in and Pikachu shocking him awake.
The Trope Namer is one of the opening lines in the initial translation of Chrono Trigger, where Crono's mom wakes him up to go to the Millennial Fair. Later, Crono has a bizarre dream where the exact scenario plays out with the Mysterious Waif instead of momma. And when you finish the game normally, the trope is again replayed, but this time with a soldier waking him up.
The Dream is replayed in a secret ending where Crono is a Reptite and his Reptite Mother wakes him up and he meets Reptite Marle in Millennium Fair.
Oddly, advertisements for the Nintendo DS re-release referenced the line verbatim... even though in the retranslation the actual phrase isn't used.
In the opening to Disgaea: Hour of Darkness, demoness Etna awakens Prince Laharl by smacking him with a number of weapons, and is just about to shoot him when he finally wakes up. From a two-year nap. Talk about a Heavy Sleeper...
In the "Etna Mode" for the PSP and DS versions she fires the shot, apparently accidentally kills him, and decides to become Overlord herself. Except he turns out not to be dead at the very end of the story.
Ends up being a different trope altogether, as the hero was raised from a young age to be a hero, and would start his/her epic quest on his/her sixteenth birthday by design.
In Dragon Quest VI, you start with a dream in which you are defeated by the big bad, and are woken by your sister. Except it's the opposite. You really did go to fight this guy, who actually isn't the big bad, but one of his minions, and you are now in the Dream World.
At the beginning of the first Golden Sun game, Isaac's mother awakens him... in the midst of a huge thunderstorm... in the middle of the night... to inform that a massive boulder is about to fall on the town.
The "main" story of the sequel begins with Felix waking up after being knocked out by a tidal wave. I guess the writers really had something against the normal laws of sleep.
Azure Dreams starts out with the Kid Hero sleeping comfortably in bed...until his female friend and his little sister awaken him by violently jumping on the bed.
In Heart of Darkness, the game opens with the protagonist being awakened by his Sadist Teacher after falling asleep in class. Oddly enough, it sounded like the teacher was actually explaining something interesting for once...
Also seen at the beginning of the online multiplayer game Monster Hunter, although nobody is there to wake your character up from his/her slumber.
In Fallout 3, you wake up to Amata telling you that your dad is gone, Jonas is dead, and her dad is trying to kill you.
In Fallout: New Vegas you wake up in Goodsprings clinic a few days after having been shot in the head.
In LucasArts' Loom, the hero is napping on a cliffside at the beginning and is awoken by a messenger nymph: "Rise, son of Cygna! It is the dawn of your 17th year. The elders await you in the council."
An odd variant in Pokémon Gold and Silver: the game effectively starts with the player waking up old mentor and expert Professor Oak and then telling him the time.
It's presumably you having a dream, one of those sorts when you start to wake up.
In Pokémon X and Y, the player is instead woken up by their mother's Fletchling bumping into them.
The main characters in Final Fantasy Tactics Advance get carried into Ivalice in their sleep. In the sequel however, the adventure starts sometime in the afternoon after school's over.
Legaia II: Duel Saga opens with a character trying to wake the protagonist with a spoon and bucket. How the player chooses to react to this sudden stimulus (wake up calmly, wake up fearfully, go back to sleep) helps determine the protagonist's attitude for the rest of the game.
The second game begins very similarly, except that the entire prologue shows how the astromech droid gets the Ebon Hawk to Peragus II. It isn't until after you've been there a while that Kreia wakes you up. Things have not gone well since your arrival.
The Overlord series subverts this, with various vicious wake-up calls. "Rub some acid into his eyes!"
Eternal Darkness starts by giving control to the player in the middle of protagonist Alex's dream, in which she's fighting off a neverending stream of zombies, probably to give you some level of the hang of fighting early on - no matter how you do, you won't take any damage and Alex wakes up, more properly starting off the game, after a set time.
Dragon Quest Swords starts out with your father awakening you with a nasty Kaboom spell and sending you on your way to the castle.
Shin Megami Tensei I begins with the hero having a dream where he is told he is the center of the balance between Law and Chaos... and then his mother yells at him to wake up. It's when he goes back to the dream that things get weird.
The original Breath of Fire subverts this; the game starts with Ryu being awakened by his grandmother... because their village is on fire.
Arguably appears in Mass Effect 2. While the game technically starts with a scene of the Normandy being destroyed, the main gameplay starts with Shepard waking up in a Cerberus lab that's under attack.
This trope is inverted before the attack: Shepard wakes up in the lab, but since s/he's not quite ready to come Back from the Dead yet, Miranda tells him/her to go back to sleep...then administers a tranquilizer so Shepard doesn't have time to argue.
Portal begins with the player being brought out of suspended animation.
In The Elder Scrolls III: Morrowind, the player character wakes up on a ship about to make landfall (Arena and Daggerfall also started with the player character waking up, but lacked the 'hey, you! Wake up!' part of this trope).
Skyrim begins with you waking up in a cart leading you to a mass execution,. (one which you aren't supposed to be a part of and is quickly interrupted by a dragon)
The Prince/Princess in Fable III is awakened by Jasper, the butler, at the start of the game.
Summon Night: Swordcraft Story starts off this way, the main character being told to wake up a seventh time.
Yuuto in Eien no Aselia starts the game out with his little sister trying to wake him up and failing, and his friend Kyouko trying to wake him up and succeeding.
Persona 3 and Persona 4 are more of a "Good Evening". In the former, one of your party members will greet you when you return to the dorm. In the latter, your cousin Nanako will greet you every night when you get home in a borderline Tastes Like Diabetes fashion. You'll still miss it when it's gone.
Subverted in Brave Soul. The hero starts the game sleeping, then wakes up to find that he's tied up in the middle of the forest.
Played both subverted and straight in Suikoden Tierkreis, the main character, Sieg, who usually oversleeps, wake up very fast in the intro because he's so excited he get to go hunting laggarts. The one who's oversleeps is his friend, who's normally the one waking Sieg up. Sieg's childhood friend, Marica, pops in after that, and surprises that her friend can wake up on his own.
Madou Monogatari: Hanamaru Daiyouchienji begins with Arle being woken up by her mother and sent off to kindergarten.
In Bastion, The Kid wakes up to find his whole world turned into a rock in the sky...
The Interactive Fiction game Punk Points started with the main character's mother waking them up from a caught-in-your-underwear nightmare for their "very first day of high school."
The title character in Tao's Adventure: Curse of the Demon Seal was woken up by his little brother.
The Clique: Diss and Make Up starts with your character being woken for their first day at "Octavian Country Day School."
Ar Tonelico 3 begins with Aoto oversleeping and getting yelled at by his boss.
The first game of the Awakening series begins with protagonist Sophia waking up from a century of enchanted sleep. As she's suffering from Laser-Guided Amnesia, her first order of business is to find out who she is (she doesn't even remember her own name) and why everyone keeps calling her 'Princess.'
Bravely Default starts with Tiz asleep in Caldisla Inn, being woken by the innkeeper. Chapters 5, 6, 7 and 8 also start in the same way.
Owen wakes up from a weird dream in the first scene of Project 0.
Parson Gotti of Erfworld is introduced this way. Except that it's not his mother, but his alarm clock getting him up at 5:18 pm to work the graveyard shift at Kinko's. Is it any wonder that he wanted to be summoned to Erfworld?
In The Demon Archives, at the beginning of Chapter 1, Tenzin gets woken up early by his AI assistant for an urgent mission.
Kung Fu Panda starts out with Po awakening from a kickass, awesome dream (complete with the amusing touch of his father's voice coming out of the Furious Five's mouths) to find out he's late for work in the noodle shop. We then get to see his daily life, from his struggle to get out of bed and the posters and action figures he's collected, to his clutziness that prevents him from throwing a throwing star (and topples him ignominiously down the stairs) and the mess he makes of the dining area with his large size. And, of course, the boring, ordinary life that he longs to escape from.