Racing Hippaul
If you talk to Hippaul's mother in one of the streets, she asks you to race Hippaul so he will get into shape. All you have to do is alternate pressing the circle and square button. After each race Hippaul levels up. Every 10 levels he reaches, his mother will reward you with a card. On the 80th level increase, you will get the Athlete Queen key item.
This can only be done before the destruction of Alexandria.
And your cards are:
10 Wyerd Card
20 Carrion Worm Card
30 Tantarian Card
40 Armstrong Card
50 Ribbon Card
60 Nova Dragon Card
70 Genji Card
80 Athlete Queen
It should be noted, that you can level Hippaul all the way up to 100. But you will get no reward for it.

Jump Rope
You can have Vivi play jump rope right from the beginning of the game. At first, it might seem very complicated, but there is a trick to getting it going. First, ignore the "!" icon. When Vivi hits the ground, press the button. When Vivi jumps, release it. Basically you are doing the moves for Vivi, rather than paying attention to the icon. For your jumping expertise, you will get some nice rewards.


20 10 Gil
50 Cactuar Card
100 Genji Card
200 Alexandria Card
300 Tiger Racket
1000 King of Ropes
If you do not like Vivi (and who doesn't like Vivi!!) you can swap him out for Eiko in the party. When you do, they will invite her to jump the rope.

Nero Brothers Gambiling
When you first return to Alexandria, head over to the weapon shop. There you will encounter the Nero Brothers. You can then ask them to play their gambling game. They will shuffle themselves to different positions. When they stop, they will ask where one has stopped. If you guess right, you will get a certain amount of gil for a reward.
This mini game can only be played before the fall of Alexandria in Disk 3. After Alexandria is destroyed, the weapon shop will no longer be there.