General synonyms:
* Ignore
* Neglect
* Overlook
* Dismiss
* Spurn
* Snub
* Scorn
* Reject
* Disdain
* Despise
More specific synonyms:
* For rules or advice: flout, violate, defy
* For someone's feelings: slight, offend, insult
* For a warning: ignore, brush off, dismiss
* For a request: refuse, reject, decline
* For evidence: discount, ignore, dismiss
The best synonym for "disregard" will depend on the specific situation and the desired level of formality.