The Moat: Six two-person teams enter the Temple, but must complete a race. The first four to complete advance to the next round. Very often, even touching the water once would cause a team to have to start again from scratch.
The Legend: Olmec tells the contestants (and the audience) about the legend in question. Invariably, the legend mentions an artifact belonging to a major historical figure which somehow "made its way into the Temple" after the owner's passing. At the end of the legend, Kirk asks where the artifact can be found, and Olmec tells the contestants which room of the temple it can be found in.
The Steps of Knowledge: A trivia round, with teams being given questions about Olmec's legend, as well as basic trivia about the places mentioned in the legend. Each correct answer lets the contestants take one step down the Steps of Knowledge; three correct answers are enough to win one of the two spots in the next round. Cue the first commercial break.
The Temple Games: A series of three competitive physical contests, usually themed around the legend, which will net the team who wins a "Pendant of Life". The first two games are worth a half-pendant each, while the last game is worth a full pendant of life (and usually determines which team wins). If there is a tie, Kirk asks a general trivia tiebreaking question. Cue the second commercial break.
Olmec's Temple: After the announcer describes the Promotional Considerations and Olmec describes the rooms, the teams get three minutes to try to make it into the temple, grab the artifact, and make it out. The temple is a two-story twelve-room maze; all doors are locked initially, and most rooms have a logic puzzle that must be solved before any doors which can be unlocked will unlock. Grabbing the artifact instantly unlocks all doors and banishes any remaining Temple Guards (and nets the team a second prize); making it out of the temple before time runs out nets you the grand prize (in early seasons, a trip to Space Camp). Cue credits.
Temple Guards: Three rooms in the Temple also have Temple Guards; you don't know where they are until the run begins. If you have a whole Pendant of Life, you can bribe the temple guard with it; if not, you are dragged out of the temple, and your partner gets to try to finish with whatever time remains. If the team that goes to the Temple has only one or one-and-a-half Pendant(s), they only have protection against two of the guards, and running into the third will usually end the game. To help them out, the teams with only one Pendant have more choices of paths to avoid the third guard, while the teams with one-and-a-half Pendants can find an extra half so that their second player can bribe the last guard with a full Pendant.
Dynamic Entry: In Season 2, Kirk slid down a climbing line to enter the set.
Early-Installment Weirdness: Season one had a much brighter, cleaner, kind of orange tint than the next two seasons, as well as the set not being covered in wildlife and billowing fog. The temple structure was also quite different; the Cave of Sighs, later the Ledges could be entered and exited, and the temple gate consisted of two large columns rather than an actual gate, as well as the actual staircase leading into the temple behind Olmec's head being significantly closer to ground level. Kirk also wore khaki shorts rather than jeans, and his delivery and commentary were a lot more rough around the edges; this might have been why the next two seasons had Olmec himself deliver the instructions for how to perform each Temple Game and how to cross the moat, which were Kirk's duties in season one. Olmec was also much less of a Large Ham in the first season.
Epic Fail: How many kids tried to put the head on first of the Silver Monkey?
In "The War Fan of the Forty-seven Ronin", one of the Temple doors wound up closing (and relocking) behind one of the contestants as they passed through it. They get ejected from the temple, their partner goes in... and cue looks of confusion and/or frustration as the door their partner just passed through is now sealed off. They eventually got the door to reopen, but by then it was too late.
One of the contestants later stated in an interview they were given both of the extra prizes as a consolation, instead of just one for not reaching the artifact.
The design of the temple created some problems for a few kids, since it would appear they designed, built, and tested the temple with adults. The Jester's Court and Shrine of the Silver Monkey were especially bad. Some kids just couldn't reach the pieces of the monkey, or the buttons on the painting.
A subversion to this occurred once, with "The Mask of Shaka-Zulu". When the player hit the switch for the door leading into the room with the mask, the door opened when it was obvious from a production standpoint (i.e. the camera wasn't ready for it and Kirk Fogg was clearly shocked) that it wasn't supposed to happen. It's credited for being the fasted successful temple run.
Gameplay Roulette: The game was played in a whopping six rounds (impressive for a half-hour show), of which only the second and sixth were fairly consistent from show to show. The other four (the three Temple Games and the method of crossing the moat) were usually different.
With all the dead ends, fake switches, rooms guarded by Temple Guards, and limited Pendants of Life (although a stock of two Pendants effectively demoted the guards to Goddamned Bats), the Temple Run easily became this on quite a few occasions.
For a few shows in Season 2, there was a Temple Game where the two competing contestants had to guess which of five holes water would squirt from, with no information whatsoever on which to base this decision.
This was, however, justified on-screen in at least one instance, as the artifact of that episode allegedly belonged to Nostradamus, making a game that tested "psychic ability" thematically appropriate.
Mook Bouncer: Temple Guards...which, it turns out, were played by stagehands. They essentially had random people snatching children on television.
Nintendo Hard: Just over one-quarter of Temple Runs were actually completed (pity the poor kids who didn't go to Space Camp or wherever else they were going). While theoretically you were SOL if you got there with less than two Pendants, a majority of the wins were with one and a half Pendants...and the highest win ratio was with one Pendant.
What made it so hard was that there was usually only one linear path, thanks to locked doors. The artifact almost always ended up in the last room you'd enter. You actually had better luck if it was on the far end of the Temple (essentially the halfway point, since after that all the doors unlocked)...and if a Guard got you, your teammate had to start over from the beginning. If it was in the middle of the Temple, like the Heart Room or Observatory, you were dead in the water.
Most winning teams picked up the artifact in the seventh or eighth room. This usually included at least one or two which involved quick objectives or simple navigation, but often a lot more in the earlier part of the show. In fact, the first two wins were almost-identical paths (the second time literally just added on the next room) of eight and nine rooms respectively, but other than navigation all the players had to do was sit on a throne and put the monkey together.
Obstacle Exposition: The basic challenges, obviously, but the most memorable part is Olmec's description of the epic journey the contestants must face to retrieve the MacGuffin of the Week.
Public Domain Artifact: Dozens of these made their way to the Temple throughout the show's run, although Legends tended to use more obscure PDAs than most.
Rule of Three: So many places in this series. Just to name a few...
Three questions on the Steps to make it to the Temple Games
Three Temple Games
Three minutes on the clock
Three Temple Guards
Three options in the upper entrance (tongues in the Room of Gargoyles, gongs in the Room of Royal Gongs, and skeletons in the Crypt)
Three Jesters' Court paintings
Three secret passwords
Three pots AND three keyholes in The King's Storeroom
Three pieces of the Silver Monkey
The list could go on forever
The Resolution Will Not Be Identified: Kirk signed off every episode with something along the lines of "Join us again for more adventure and another great legend of the Hidden Temple!" The exception was "The Lion-Headed Bracelet of Chandragupta", where the phrase was cut for time. Popular fan theory was that the "Chandragupta" episode was the last one produced, before Nickelodeon revealed that it was actually "The Jewel-Encrusted Egg of Catherine the Great".
Stealth Pun: A lot of the artifact placements. For example, the Thornwood Gavel of Judge Roy Bean was placed in the Jester's Court, and the Dried Apple of William Tell was placed in the Room of the Ancient Warriors. Because of the various room changes throughout the show's run, some placements were more subtle still — the heart-shaped Lucky Pillow of Annie Taylor was placed in Medusa's Lair, which was a replacement for the Heart Room.
Theme Park Version: Most of the legends were actually balancing on the thin line between bowdlerization and sloppy research, usually subtly modified so that the character in the legend lost something that has somehow wound up in the Temple...when in reality the item doesn't exist, was never lost in the first place, or was incredibly generic (it's very likely that Harriet Tubman used a walking stick at some point in her life, and anybody who lived before 1910 is going to have used horseshoes).
Timed Mission: Most of the challenges were like this, but the most famous was definitely the three-minute Temple Run.
In certain situations where there are more unavoidable temple guards than pendants available, a team might not be able to win at all—especially when they did something as devious as stick a Guard in the very first room of the temple.
Temple Layout #5 was never beaten. Oddly enough, it was used in the very first produced episode before being brought back later in the season.
The times players lost due to glitches, such as the aforementioned door being relocked.
If you were doing well enough, it was possible to only be able to lose by running out of time. Even if the Temple layout forced you to run into all three Guards, the only way to lose would be to run out of time because you essentially have four hits. This also depended on the layout of the Temple, and if your partner got klutzy in the Shrine of the Silver Monkey or got stuck in the Jester's Court...
Having the first player taken out of the Temple in the last room before the artifact was even worse — only one team won under this condition, and they only had to go through six rooms anyway (most teams had to pass through anywhere between seven and nine to get to the artifact).
There were also deadly configurations, mostly involving the central pillar. Nobody won when the artifact was in the bottom room of this pillar (and only three reached their respective artifacts), and nobody even managed to reach an artifact in the center room if they had to start on the top floor (although two teams did win after starting on the bottom floor). By Season 3, when the Temple had more time-consuming objectives, nobody won when an artifact was in the top room of the pillar. There were four wins there in the earlier seasons, but if it puts things in perspective all four were done without the second player even having to go in (meaning the team only ever ran into one Guard).
Wall Master: Temple Guards sometimes hid like this. Usually, if not always, you never knew there was a Temple Guard in a room until it was too late.