Unlock Classic Ninja Gaiden:
Give 50 Scarabs to Muramasa. You will get the Ninja Gaiden disc, which can be used at the arcade machine at Han's Bar's first floor.

Unlock Classic Ninja Gaiden 2: The Dark Sword of Chaos:
Achieve a Master Ninja rank in all levels (Normal Difficulty).

Alternate method:
First unlock Ninja Gaiden. Get to the Clock Tower Plaza of Tairon. Get up on the ledge above the multi-colored door that goes to Pleasure Street (right where the switchis to unlock the door).

Use your bow, and shoot the face of the clock tower across the street. Hit it dead on, and a treasure chest will appear on a building on the other side of the street.

Get off the ledge, and go through the doorway across the street with the stairs, and climb up and open the chest to get the Ninja Gaiden 2 disc.

Unlock Classic Ninja Gaiden 3: The Ancient Ship of Doom:
Achieve a Master Ninja rank in all levels (Hard/Very Hard Difficulty).

Alternate method:
First unlock Ninja Gaiden 2. Get to the Peristyle Passage (it's the ceremonial room in the Aqueducts, just before you fight the giant bird).

It is next to the Hall of Balance. Do a triangle jump up to the top of the broken pillar and instead of a Scarab, you will find the Ninja Gaiden 3 disc.

Unlock Costume:
Complete the game on normal or hard difficulty. Then hold L while selecting the "New Game" option at the opening menu to wear the Ninja Of The Future costume.

Unlock Plasma Saber:
Complete the game on normal difficulty. A new sword called the Plasma Saber will be unlocked.

Skip FMV Sequences:
Press Start, A, Start to skip a FMV sequence.

Unlock All FMV Sequences:
Complete the game on normal or hard difficulty to unlock all FMV sequences.

Unlock Very Hard Difficulty:
Complete the game on normal or hard difficulty to unlock the very hard difficulty setting.