Story mode rewards  -  Beat story mode with any character to get the following rewards

Command attack minigame Beat story mode 2 times
Tekken Bowling minigame Beat story mode 3 times
Theater mode Beat story mode 1 time

Tekken Dojo - While playing through Tekken Dojo, several featres can be unlocked. The majority are unlocked as you are through Tekken Dojo, while some are unlocked after completing Void Dojo.

3,000,000 G Awarded after clearing the Ranking Tournament in Void Dojo.
Burning Auras Beat Time Attack
Heaven Dojo Clear Void Dojo. Must beat Ranking Tournament and Jinpachi.
Jinpachi Ghost Unlocked Clear Void Dojo. Must beat Ranking Tournament and defeat him.
Life Auras Play through Fire and Wind dojo.
Tekken Dojo Gold Rush Unlocked while playing through Wind Dojo.
Tekken Dojo Roulette Battle Unlocked while playing through Void Dojo.
Tekken Dojo Survival Unlocked while playing through Fire Dojo.
Tekken Dojo Time Attack Unlocked while playing through Water Dojo.
Tempest Auras Play through Earth and Water dojo.

Stage 0 in Dojo Mode  -  Complete all 6 stages in Dojo mode to unlock stage 0. In this mode, you can play against all downloaded ghost characters whenever you want.

Movies  -  There are few unlockable movies other than the ones gotten by playing through Story Mode with each fighter.

2006 E3 trailer Beat command attack 5times around 1min 30 sec
Opening Movie Console Part 2 Earn more than 5000G in one round in Gold Rush Mode
Tekken 5 Opening Movie (Console Version Pt.1) Beat Time Attack
Tekken Dark Resurrection Opening Movie (AC Version) Beat Survival Mode

Play as Panda  -  To play as Panda. Select Kuma. Instead of pressing X, Press O. You will play as Panda instead.
Kuma and Panda have two different stories.