Logo Fun: (Uncomfirmed)
Source: GamePro - April 1996 - Page 126
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When the SEGA logo appears, you can control Vectorman.  Jump off the logo to the right and fire upwards - just to the right of the "A" in "SEGA".  When the hidden monitor explodes, jump up to it and get a hidden power-up.  Now you can destroy the SEGA logo when you shoot it.

Invincibility: (Unconfirmed)
Source: GamePro - May 1996 - Page 116
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At the title screen, select Options, then select jukebox.  At the jukebox menu, press Button C to play the tunes in the following order: 3, 12, 17, 2, 2, 10, 2, 7, 7, 11.  When you start a game, you will be invincible.

See Vector Numbers, Five Little Dots, Slow Down When Hit, and Skip to Stage 5: (Unconfirmed)
Source: GamePro - May 1996 - Page 120
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To perform the following tricks, start a game and pause it.  Then while the game is paused, enter any of the following cheats:

See vector numbers: Press Button B, A, Left, Down

See different vector numbers: Press Button B, A, Left, Left

Put five little dots around Vectorman: Press Button A, B, A, C, A, B, B

Slow Down when hit: Press Down, Right, Button A, C, Up, Left, A.

Skip to Stage 5: When the game starts and Vectorman is teetering on the Sega logo, jump under the logo and shoot it 24 times.  Then jump up and hit his head on it 12 times.  Now you can play a bonus game where letters fall from above.  Catch 90 letters and you start the game at Stage 5.

Orbot's Private Options Screen: (Unconfirmed)
Source: GamePro - April 1996 - Page 118
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At the Options screen, press Button A, B, B, A, Down, A, B, B, A.  A new screen appears named "Refus Q. Orbot's Private Options Screen" that lets you increase health and lives, power up your weapon and select and level.

Game Genie Codes
Source: GamePro - May 1996 - Page 109
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AXKT - AA8C - Infinite rocket-boost jumps
R0RA - N60Y - Weapons don't run out
RGNA - A61L - All health power-ups max out health
AL8A - AA72 - Invincibility
F4PT - AA3T - Infinite Time
C49T - AA28 - Infinite Lives
B8MT - AACE - Start on Twist and Shout level
CCMT - AACE - Start on bonus level