Formal/Neutral:
* Compliant
* Docile
* Submissive
* Deferential
* Yielding
* Amenable
* Tractable
* Pliable
Positive:
* Respectful
* Law-abiding
* Well-behaved
* Disciplined
* Rule-following
Negative:
* Subservient
* Passive
* Unquestioning
* Blindly following
* Uncritical
* Spineless
Informal:
* Goody-goody
* Yes-man/Yes-woman
* Toeing the line
* Playing by the rules
Literary:
* Pliant
* Supple
* Yielding
* Obsequious (excessively eager to please)
The best synonym for "obedient" will depend on the specific context and the tone you want to convey.