Enter the following at the Cheat Menu:

STICKMAN  Unlock Stickman Spidey 
WEAKNESS  Full Health  
LEANEST   Unlock Everything 
GLANDS    Unlimited Webbing 
EGOTRIP   Pulsating Head 
SECRTWAR  Unlock Symbiote Spidey Costume
MIGUELOH  Unlock Spidey 2099 Costume 
TRISNTNL  Unlock Captain Universe Costume
ADMNTIUM  Invulnerable
CINEMA    Movie Viewer 

GameShark Codes

Invulnerable
DC8882FE00000001
  
Unlimited Webbing
C28BE6D900000001 
  
Stickman
DA388DBD00000001
  
Pulsating Head Mode
88F38C2100000001
 
Unlock Storyboards
8B70833120703FC2
7805DD3300000102
  
All Levels Unlocked
8B70833120703FC2
A1DB5FA000000101
C06AA9C9E06F5041
E0507061
 
Unlock All Costumes
8B70833120703FC2
487A11F800000FFF
  
Unlock All Character Viewer
8B70833120703FC2
8D134331FFFFFFFF
 
Unlock All Movie Viewer
8B70833120703FC2
D8184DEEFFFFFFFF

Unlock All Comic Collection
8B70833120703FC2
10E4D8A0FFFFFFFF
 
Unlock All Game Covers
8B70833120703FC2
640BA570FFFFFFFF
 

Thanks to Revolution reader nico!