General:
* Desert
* Forsake
* Leave behind
* Give up
* Relinquish
* Disregard
* Neglect
* Drop
* Quit
More specific:
* Abdicate (for a position or responsibility)
* Abjure (for a belief or practice)
* Defer (for a task or responsibility)
* Reject (for an idea or plan)
* Renounce (for a claim or right)
The best synonym for "abandon" will depend on the specific situation and the intended meaning. For example, "desert" implies a deliberate act of leaving someone or something, while "forsake" suggests a more emotional decision.