Cheat Codes:

Enter during game:

GH44 -- Invincible On/Off. 
DDB4 -- Time Limit Off/On (no time bonus if off when episode ends). 
DD6D -- Episode 1. 
DF6D, CKBGMM -- Episode 2. 
D46D, SCTWMN -- Episode 3. 
D76D, MKBRLN -- Episode 4. 
D06D, LBLNRD -- Episode 5. 
D96D, JMDKRK -- Episode 6. 
D16D, STGRTN -- Episode 7. 
D66D, SBBSHC -- Into The Canyon 1. 
DC6D, DBKRRB -- Episode 8. 
DA6D, MSFCTS -- Into The Canyon 2. 
D26D, KMGRBS -- Episode 9. 
D36D, SLJMBG -- Into The Canyon 3. 
DE6D -- Episode 10. 
FD6D -- Episode 11. 
FF6D -- Episode 12. 
F46D, TGRTVN -- Episode 13. 
F56D, CCLDSL -- Episode 14. 
F66D -- Episode 15. 
G00D, STCJDH -- Episode 16 (none of the cheat codes work in this episode). 
F00D -- Ending Sequence. 
SLS, BBPAN, SHARK -- Bubsy slides, flys or jumps in weird, uncontrollable ways. 
Saved Game Hex Cheat Codes (the only way to cheat in episode 16)

Start a Super Bubsy game, hit Escape, choose Options, save a game, edit the saved game with a hex editor. Byte 18 hex is the number of lives. Enter any hex number up to FF hex. The largest number displayed during the game is 99, so if the the value entered is 64 hex or higher, the 99 will continue to be displayed until the actual number of lives is decreased to below 99.

Byte 20 hex is the episode number. Enter any hex number up to 14 hex. 13 hex is the last playable episode (and the one in which no cheat codes will work). 14 hex is the ending sequence. Bytes 34 hex and 35 hex are the time remaining. These values are repeated in bytes 38 hex and 39 hex (reason unknown). Apparently the highest value accepted is FF hex in bytes 34 hex and 38 hex and BA hex in bytes 35 hex and 39 hex. Putting very high values in these locations will result in items from the game being displayed in the time remaining area instead of numbers and a much larger time bonus at the end of the episode.