If you haven't seen the old rules yet, here they are

Old Rules:
-If you run out of lives, it's automatic game over. 
-No getting extra lives, 100 rings or 50 thousand points don't count
-1P only, but CPU tails is allowed because CPU Tails is an idiot.
-Post your results on this thread

These are the new rules, that make it easier as the game goes, such as completing zones. The old rules will still exist.

New Rules:

-No shields 
-No 100 rings, if you get it you must lose your rings to make it under 100. 
-No speed sneakers
-No invincible boxes
-No extra live boxes a
-No skipping zones
-No chaos emeralds or Super Sonic
-No debug
-No level select

Seems hard, huh? Well that won't be the problem: REWARDS! Rewards are things you will get for completing a zone.
Full list of rewards:  (Sorry about the font change, I tried to copy and paste something and I got a different font)

Pass Emerald Hill: Shield Box
Pass Chemical Plant: Extra Life Box, if you find one
Pass Aquatic Ruin: Speed Sneakers
Pass Casino Night: Invincible Box
Pass Hill Top: 100 Rings allowed
Pass Mystic Cave: Allowed tails to do the dirty work on bosses and enemies.
Pass Oil Ocean: Allowed to skip one zone, and one zone only (Cannot be death egg)
Pass Metropolis: Save States
Pass Sky Chase: The Secret Wing Fortress Item Box
Pass Wing Fortress: Nothing
Pass Death Egg: You beat the nuzlocke! Congrats! Level Select, Debug
Get all 7 chaos emeralds (you sneaky bugger): Nothing, jk. Debug Mode

How I did (Different font again sorry):

EH1: Accidently got shield box, later got hit by an enemy and lost it.
EH2: WHY DID I GET THE SPEED SNEAKERS, WHY..... I got hit once so it was worth it
CP1: Took lower route, got upset
CP2: Shortcut, accidently got invincible box and 100 rings, I feel ashamed
AR1: Took high route luckly and got into the water once but escaped quickly
AR2: Almost drowned twice when taking the lower route: Took it slow. Boss was too easy
CN1: Woo, speed sneakers. *broom broom through the level omg lower route again, noooooo*
CN2: Died twice on the boss and once on the moving floor. (3 lives remaining)
HT1: Survived the whole time and got through the annoying moving floor section with no scratch
HT2: Rising lava= Easy. Boss= Easy. Lose Rings after defeating the boss= Okay
MC1: I officially hate the light enemy.
MC2: I got this, going to avoid the spike pit of death. Tails did to ya- WTF TAILS WHY'D YOU DO THAT YOU MADE ME FALL THROUGH THE FLOOR AND FALL INTO THE PIT WTF [2 Lives left]
OO1: Lower routes made me barely got through but I passed
OO2: *gets hit* Oh, come on! *hit again* Oh, come on! *dies* Oh, come on! [1 Life] I hate these lower routes, I give up, goodbye attempt 3. *jumps into spikes* [0 lives left, game over]

How did you do? Leave your post here about how you did.