And here are the games. If anyone has any other suggestions, or has come up with a game, include a full write-up including ages it can be played in, number of players, and a description of the rules and I'll add it in!
Location: Bevin
Players: 2-5
In each Bevin-style Neighborhood, you will find an Ahyoheek table at the bottom of the stairs. This is a game playable by 2-5 players and is very similar to Rock, Paper, Scissors. To begin, the players sit at the station of their choice. The buttons on the table are labeled with a Pen, a Beetle, and a Page. In each round, all the players choose one of the symbols. Once everyone has chosen, the round is over and points are totaled.
Pen beats Page
Page beats Beetle
Beetle beats Pen
To figure out your score, you add one point for each symbol played that you beat, and subtract one point for each symbol played that beats you. Same symbols have no effect. Note that you can have a negative score. The person with the highest score wins the round, and they get a marker indicating which symbol they won with. The first person to gain three of the same markers wins. In the event of a tie, the person with the highest total number of markers wins. A continued tie causes the remaining players to participate in sudden-death matches until one of them is victorious.
Thanks goes to DPWR's Games: Ahyoheek article for refreshing my memory on tiebreaking.
Location: Anywhere
Players: 2+
Sardines is a game dating back at least to UU and possibly back into Prologue. It is a variation of the popular game Hide-and-Seek. It begins with one person designated as the "Hider". This person will find a hiding spot in whichever age has been chosen to play in and will not move once there. They will then notify the other players to begin the game. You can sit or stand to improve your hiding, but you cannot change spots once the game has begun. The remaining players are designated "Seekers". These players will remain stationary while the Hider is getting into position, and then will seek out the Hider. Each Seeker is an independent player, meaning they work alone, though teams may be formed if decided before-hand.
Upon finding the Hider, the Seeker will not notify others of their location, but rather will stand on top of them (ideally getting the player models to occupy the same space). This continues until all Seekers but one have found the hiding place. When the last Seeker has found the hiding place, the game is over, and the last Seeker becomes the Hider for the next round. Use of the "/autoshout" command is recommended if playing in an age where 10+ people are present, so everybody can read the chat. Places that can only be reached through glitches in the physics system (such as above the rope bridge in Ae'gura) are illegal hiding places and cannot be used.
The name "Sardines" comes from the comparison of a bunch of avatars standing in the same exact location, in the same orientation, to a tin of Sardines.
Location: Gahreesen
Players: 2-4
This game involves the Great Wall in the second tower in Gahreesen. This game is not currently playable, but is included here for completeness. If The Wall ever becomes available, this post will be updated to include its rules.
Location: Er'cana
Players: 1 (plus neighborhood helpers)
The Pellet Challenge involves accumulating as many pellet points as possible in one hour on a single avatar. Generally done with the participation of other neighborhood members so as to allow the player to visit multiple Er'cana's, and accumulate the points from each. Points are then compared against members in competing neighborhoods.