So you're playing a game and you reach a critical point in the story. Something bad happened, and things got worse. Maybe the hero just took a No-Holds-Barred Beatdown from the Big Bad, or maybe the world has sustainedmassive damage. Perhaps the time has come to take immediate action to stop the Big Bad from carrying out his plot.
Alternatively, there is a lull in the story (or Exposition Bomb), or another incongruous moment, like after a conversation, when things are about to get worse.
Either way, either something big has happened, or something big is about to happen.
Cue the Ominous Save Prompt, which often looks or works different from an ordinary save prompt.
Often used in a Downplayed manner: a character says that the game should be saved, (e.g. "We need to double check our equipment" along with a "Ready to go?" prompt,) but the Player must still call up the save menu normally.
Getting one of these in The Very Definitely Final Dungeon is a sign that the Final Boss is nigh. Granted, these could also show up in the Disc One Final Dungeon right before you fight the Disc One Final Boss (or, rather, not fight him.)
Subtrope of Suspicious Videogame Generosity, in this case letting you know you should save before (and/or after) the rough patch. Indeed, for most games where saves are usually automatic or handled by checkpoint, the appearance of any save prompt qualifies for the Genre Savvy player.
Would you like to save before reading the Examples? You really should.
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In the Interactive Fiction game Firebird, just before the PC is about to set off on the main adventure, he thinks about how this would be a good time to say a prayer for the journey ahead. Cue the unorthodox save prompt: "Would you like to save your soul?"
The Infocom Interactive Fiction game Wishbringer prompts you to save before playing the "Transmatter" arcade game. Standard for the genre, and not the only situation where the wrong actions make the game Unwinnable, but they ramp up the ominous factor several times by asking if you really want to play and having the other gamers go quiet.
If Ciel ever asks you if you want to save in a Mega Man Zero game, something is about to go down (assuming it hasn't already).
Role Playing Game
MOTHER 3 prompts you to save at the end of each chapter, after the chapter epilogue has played and the screen has gone black. A couple of the save frogs also have dialogue where they really recommend that you save now.
Similarly, Disgaea games allow you to save after every chapter, either after the plot for the next chapter has been set up or before a twist will take place. The fact that there's no music and a mostly-black screen on the between-chapter save menus only adds to the ominousness.
Parasite Eve prompts you to save at the end of each day, and also does so after a particularly lengthy cutscene (and just before a particularly difficult battle).
The PlayStation 1-era Final Fantasy games did this at the end of each disc, which were almost always immediately following major plot events (though a very obvious reason for it is simply a failsafe in case something goes wrong during the disc swap.)
The PC Porting Disaster of Final Fantasy VII seemingly missed that part and set the save-points immediately after the disc swap. Which would often fail thanks to the game's buggy disc-detection, forcing you to replay 15-30 minutes from the previous save point.
Final Fantasy XII would, at certain save points, recommend that you use a second save slot for that save, instead of overwriting your old one. This generally happens when you've passed a point of no return since the previous save and there's still some trouble to deal with before you reach the next safe area.
It had one rather odd example, though. Just before you head into the Raithwall's Tomb area, the game prompts you to save. It likely does this because there's a boss fight as soon as you step into the courtyard in front of the tomb, but one has to wonder why they didn't just stick a save crystal there instead.
Final Fantasy XIII give you the option to save at the end of each chapter. Since there's usually a significant cutscene at the start and end of each chapter, this is just a good idea, especially on the (three-disc) 360 version, which has you swap discs after chapters 4 and 9 (notably, the disc swap happens after you save, just like the PS1 games).
The remake of Wild AR Ms 1 normally gives you the traditional save points. But there are two occasions in which the act of entering a door causes a save prompt to appear. Both are preludes to fights with the Big Bad, and both of them are definitely warranted.
Near the end of Mario & Luigi: Partners in Time, after blowing the Princess Shroob's Flying Saucer out of the air, Stuffwell urges the brothers to save the game before going after the princess, and also announces that he is capable of bringing them back in time to before they entered the final room, in case they wanted to go back to search for missing items. Predictably, after leaving the area with the save block, the final battles begin.
Glory of Heracles DS will stop you at the start of dungeons with a message to the effect of, "You are about to enter a very dangerous area. Save?"
During the Present Day chapter of Live A Live, after beating the six opponent wrestlers, the game asks if you would like to save. Sure enough, you face down the chapter's final boss Odie Oldbright immediately afterwards.
Certain dungeons in Pokemon Mystery Dungeon Explorers are divided into multiple sections, with a Kangaskhan Rock waiting for you at a 'safe point'. While normally Kangaskhan Rocks let you store and take out items, these variations only permit you to save. In Sky's second bonus chapter, Armaldo explictly points out that finding one inside a dungeon means there's probably a boss up ahead.
OFF asks you to save the game whenever you beat the guardian of the zone. If you revisit that zone, you will see a very good reason why.
Dink Smallwood mods do this on occasion, varying by author. One rather strange instance in As Good As Eternity involved a fountain outside a food storage building full of monsters (instead of the normal save machine) and the man on the top floor telling you to "wash your hands in the fountain" as part of food safety procedure.
Sigma Star Saga gives you a somewhat-unneeded one of these (as you would probably have remembered to save before heading into the battle in question, anyways).
Stealth Based Game
Metal Gear loves this trope. It even has one instance in which you are warned against saving.
Right after The Reveal, Silent Hill 2 features a long hallway with nine save points right at the end game. The final two boss fights are right through the door past the save point.
In Silent Hill 3, the room that lies right before the final boss fight features a very conspicuous save point.
The Resident Evil games that use more than one disc had this, and treated it as a "free" save, as it didn't cost you an Ink Ribbon. In Code Veronica, it also didn't count against your rating, so it was the only place you could save and still get a perfect score.
Prior to fighting the Black Guardian in Eternal Darkness, the game directly tells you to save.
The Witch's House. Right when Ellen's ruined body starts stumbling towards you, the game prompts you to save even though the cat's dead body (your save station) was right outside the door. After the save point, you will die a lot. Also, this is the part where you perform the action that decides your ending.
In Scott Pilgrim, being a world run on Rule of Cool and Video Game Tropes, has a save point in a corner right before a fight with the 3rd evil ex. Note that this is the first instance of a save point within the book.
Scott at first wonders what it is, and is told that "It looks like a save point." He reasons that if it is a save point, he has to go save because something really bad might happen.
Marble Hornets (er, sort of) - Jay learns that Jessica has all the symptoms of being stalked by the Operator, and decides that they really need to leave the creepy, apparently-deserted hotel. Unfortunately, he stops to upload this to his YouTube account before getting the hell out of there, leaving the fanbase dreading the next entry. By the time he's ready to go, not only has Jessica vanished into thin air, but the Masked Man has shown up again.