Secret Locations
There are a number of secret locations in FFX that you can access by searching the world map with your airship, or by simply entering passwords.

Airship Coordinates
Use the following coordinates on the airship world map, then press X when you've found the spot. These coordinates are approximates, so move the cursor around a little and press X repeatedly to find the hidden areas.

    * Baaj Temple -- X:14 Y:60 (find Lulu's Onion Knight and Anima here)
    * Sanubia Desert: X:15 Y:41 (find Tidus's Ascalon)
    * Omega Ruins: X:74 Y:36 (battle Ultima Weapon, steal items, and find spheres)
    * Besaid Falls: X:31 Y:73 (find Kihmari's Dragoon Lance)
    * Mi-I'hen Ruins: X:34 Y:58 (find Rikku's Sonar here)
    * Battle Site: X:42 Y:57 (find Lulu's Phantom Bangle here) 

Airship Passwords
You can also input passwords to uncover secret locations. These passwords are hidden throughout the game in Al Bhed -- but if you can't read it, here they are (note that they have to be entered in all caps):

    * GODHAND -- Let's you go to lower Mushroom Rock Road where you will find Rikku's legendary weapon.
    * VICTORIOUS -- Enter this to access a secret area in the ruins of Besaid. Climb the tree to get your hands on Rikku's powerful Victorious armor.
    * MURASAME -- Another secret area in the ruins of Besaid. You will find Auron's Murasame (ability: One MP Cost) here. 

Free Chocobo Rides
Go to the Calm Lands and become a chocobo trainer by talking to the female chocobo rider (leave the area and come back in on foot if she's not there). Complete the Wobbly Chocobo training exercise (cross the finish line with 12.8 seconds or less) and you will be able to ride a chocobo for free in the Calm Lands by talking to a trainer.

Character Overdrives
Tidus
Tidus learns new Overdrive techniques simply by using his old ones. You have to successfully pull off an Overdrive for it to count.

    * Spiral Cut (available from start)
    * Slice & Dice (perform 10 Overdrives)
    * Energy Rain (perform 30 Overdrives)
    * Blitz Ace (perform 80 Overdrives) 

Yuna
Yuna's Overdrive lets her summon an aeon with its Overdrive gauge completely filled. She is not able to learn specific techniques like the other characters.

Auron
Collect the Jecht, Auron, and Braska spheres that are hidden throughout Spira to teach Auron new techniques.

    * Dragon Fang (available from start)
    * Shooting Star (find one sphere)
    * Banishing Blade (find three spheres)
    * Tornado (find all 10 spheres) 

Locations:

    * Jecht Sphere: Macalania Forest (after Spherimorph fight)
    * Jecht Sphere: Besaid Village (next to temple)
    * Jecht Sphere: S.S. Liki (on the bridge in Besaid)
    * Jecht Sphere: Luca Stadium (basement level A)
    * Jecht Sphere: Mi-ihen Highroad (southern Old Road)
    * Auron's Sphere: Mushroom Rock Road (cliff)
    * Jecht Sphere: Moonflow (South Wharf)
    * Jecht Sphere: Thunder Plains (southern part)
    * Jecht Sphere: Macalania Woods (southern area)
    * Braska's Sphere: Mt. Gagazet (Mountain Trail) 

Kihmari
Kihmari can learn new techniques from his enemies by using the Lancet ability. Try this move on every fiend you meet (or switch Kihmari in whenever one of the following attacks is used on you) to build up his repertoire of Overdrives. Be sure to learn his most powerful move, Nova, from the Omega Weapon.

    * Jump
    * Fire Breath
    * Seed Cannon
    * Self-Destruct
    * Thrust Kick
    * Stone Breath
    * Aqua Breath
    * Doom
    * White Wind
    * Bad Breath
    * Mighty Guard
    * Nova 

Wakka
Wakka is a Blitzball player, so it's only fitting that his new techniques are unlocked by playing Blitzball. By winning in the League and Tournaments you can expand your repertoire to the following overdrives:

    * Element Reels (available from start)
    * Attack Reels
    * Status Reels
    * Aurochs Reels 

Lulu
Lulu's Fury Overdrive allows her to cast any black magic spell multiple times in a row without losing MP. Rotate the right analog stick clockwise as fast as you can to increase the number of attacks.

Rikku
Rikku's Overdrive ability allows her to mix two items together for devastating attacks or helpful potions.