Go Wait Outside

So, our hero has just given the blacksmith or healer some unobtanium or rare plant he gathered from the far reaches of Slippy-Slidey Ice World to make into something he can actually use in battle. The NPC tells him it will take a while "so wander around and come back."

Our hero, ever impatient to get on with his epic quest, comes right back inside after walking out, probably to bug the NPC with taunts of "Are You Done Yet??" Amazingly, the NPC is not only finished with the commission, he asks what took our hero so long to get back.

This is a video game trope in where the game expects the player to Talk to Everyone in town while waiting for the Item Crafting NPC to finish, but the actual programming causes the Event Flag for them to finish to turn once the player leaves the building. This leads to the hilarious situation where the NPC can apparently finish the Infinity+1 Sword in less than half a minute.

If the game forces the player to finish a dungeon or some other plot event before the "commission" (likely some Plot Coupon) is finished, that's a Broken Bridge.

Action Adventure

 * The Legend of Zelda Phantom Hourglass has a convenient distraction in the form of a sub-plot resolution when the blacksmith is forging the Phantom Sword.
 * Link to The Past did this as well with the Level 3 Sword. If you left the building and immediately returned, the smiths wouldn't be finished, but all you have to do to trigger the flag is leave the larger map screen where the shop was located.
 * A faster way is to get there in the Dark World, whip out the mirror, go to the Light World, drop the thing off, then step in your mirror portal and immediately warp back. All done!
 * Averted in Majora's Mask, since the blacksmith requires a full day to reforge the sword. It's ready by dawn. Similarly, you have to wait a few days for Biggoron's Sword to get finished in Ocarina of Time.
 * With the Biggoron's Sword you can just use the Song of Sun multiple times to make the days go really fast. More Biggoron, he worked FAST.

Adventure Game

 * The Healer in the VGA remake of Quest for Glory I does this when making the Dispel Potion. In the original EGA version, however, the healer actually does take an in-game day to make the potion for you, as does Salim in Quest for Glory III.

Hack and Slash

 * In Diablo 2, Act 3, Alkor the alchemist tells you to busy yourself while he's experimenting with the ashes of Ku'yleh, but clicking on him again is more than enough.

MMORPGs

 * A variant in World of Warcraft is equally silly. You're told to wait, but three seconds later he's done. However, there's a good reason it doesn't happen for more than a few seconds in WoW. Griefers could simply log off and wait in the building to prevent anyone from turning in quests to that NPC.
 * Quite a few contacts in City of Heroes have dialog that reflects passage of time in between missions in a story arc, even if you select the next mission right on the heels of the last. "I'll have this mysterious substance analyzed to find out what it is. Good, you're back. I had that stuff analyzed and..."

Role Playing Game

 * Final Fantasy IV has one of these when a blacksmith is forging you a weapon. The flag triggers as soon as you go to the moon.
 * Attempting to breed chocobos in Final Fantasy VII involves "wait time." The flag is triggered once you fight about ten battles at any spot.
 * In Final Fantasy VIII, after finishing the first half of the Shumi Village sidequest (when Attendant is assigned to help sculpt Laguna's statue), the quest will not continue until you exit to the world map and re-enter the village.
 * The fossil reviver in all the Pokémon games. Sometimes you actually do need to walk around a bit, but it's just as common that you can walk out and into the building.
 * Averted in the Day Care Center, where you must spend some time walking to get two paired-up Pokemon to yield an egg.
 * Also averted with the Apricorns in the Generation II games--after giving the Apricorns to Kurt, you have to wait a day before coming back to retrieve the special Poke Balls made from them.
 * The blacksmith in Golden Sun: The Lost Age. In this case, you also have to leave the entire village.
 * Instead of leaving the town, you could also just spend the night at the inn or walk into the sanctum.
 * The end trigger in the 'Mission's Brother' quest in Knights of the Old Republic is a particularly amusing example: the trigger for the next conversation is you leaving the zone, but because of how the despawning system works, you can overtake Griff on the way to the door, come back in and be told he skipped town while he's still visible behind you.
 * If you ask Ajuur to set up a duel with Bendak, it "takes some time" to bribe officials etc. If you have that conversation late enough in the main Taris storyline, this is apparently just long enough for you to get to the door and back.
 * In Mario & Luigi: Superstar Saga, the Hammerhead Bros. say this to Mario and Luigi before they make hammers from the Hoohoo Block that fell into their workshop.
 * As well as when the bridge is being repaired so you can get said block. Thought somewhat of an aversion as you actually have to Talk to Everyone before the event flag will trigger.
 * Common in the Tales (series). Whenever it is not used, it's usually to cram in a cutscene or another dungeon for you to loot while it's being made.
 * In The Elder Scrolls III: Morrowind you do need to wait for several days for the statue you ordered to finish the construction, but you need to exit the building if you try the rest method, or else the sculptor won't go make it.
 * Being a game that is aware of its own internal calendar, and likes to use it, The Elder Scrolls II: Daggerfall has the player submit his worn weaponry to a merchant who has skill repairing weapon items and being asked to come back in x days when it's done. In fact, it takes x+1 game days to be repaired as the merchant doesn't even start on it until the next day.
 * Neverwinter Nights is all over this trope.
 * Ultima Underworld features a blacksmith character who will repair your items. The trope is averted by requiring X REAL TIME minutes to accomplish the repairs, and then de-averted via (game) time-speeding tricks like sleeping (unless your character isn't tired).
 * Why is it a de-aversion? The requirement for X real-time minutes is because time in the UW games isn't compressed (like it is in almost every other RPG), so an hour of game time takes an hour of real time. However it's only natural that sleeping for 3 hours would mean the item's ready (none of the waits are longer than one hour) because the game time clock's been advanced by 3 hours.
 * The Witcher also uses it sometimes; in at least one quest, when Geralt is supposed to talk to an NPC the following day, it suffices to change location (for instance, enter and quit a building). It happens two more times during just that one quest.
 * At one point in Dubloon, Timber has to built another ship while on Pyrite Island. It takes as long as you re-enter part of the island where he is.
 * Averted in Persona 2 with the sweepstakes magazines. After handing them over to the friendly NPC who will fill them out and mail them in for you, you have to go kill some time in a dungeon before any prizes will arrive.
 * Also in Persona 3 because the game follows a strict calendar time outside the dungeon, where each day is divided into time periods that some actions will advance. The antique shop owner always requires a day (or two, for everyone's ultimate weapons) to produce requested weapons.
 * And in Strange Journey. There's a dwarf in one area who will make you special weapons if you bring him the right forma, but it takes him a set number of moon phases to finish.

Shoot'Em Up

 * When you give Naomi the Military Secret or in No More Heroes, she tells you to come back later for a new beam katana. "Later", of course, means "as long as it takes to leave and come back in"... though they're so expensive it's more like "leave, do a few assassination side-jobs, come back in".

Turn-Based Strategy

 * Shining Force II has this with the Mithril weapons.

Wide Open Sandbox

 * A solid example appears in the game Prototype, where the resident Doc has to analyze a bunch of genetic material and come up with a functional cure to a weaponized cancer designed specifically to kill Alex Mercer, who is infected with a strain of virus which is also a weaponized super-disease. The man does it in as long as it takes you to walk back into his under-equipped morgue.