General occurrences:
* Occur: This is a good general replacement for "happen" in formal writing.
* Transpire: This implies something that unfolds or becomes known, often with a sense of mystery or intrigue.
* Take place: This emphasizes the event itself and is often used for planned or scheduled occurrences.
* Come to pass: This is an older, more formal way of saying "happen," often used in historical writing or to emphasize fate or destiny.
Unexpected or unplanned occurrences:
* Befall: This suggests something happening to someone, often with negative connotations.
* Arise: This suggests something coming into existence unexpectedly, usually with a problem or issue.
* Emerge: This implies something becoming visible or known after being hidden or concealed.
* Eventuate: This emphasizes the result or outcome of an event.
Specific contexts:
* Materialize: This suggests something becoming real or concrete after being abstract or theoretical.
* Manifest: This emphasizes the outward expression or appearance of something.
Ultimately, the best word to use will depend on the specific context of your writing. Consider the tone, the meaning you want to convey, and the level of formality required.