General curiosity:
* Inquisitiveness
* Interest
* Eagerness
* Desire to know
* Wonder
* Thirst for knowledge
More intense curiosity:
* Inquisitive
* Nosy
* Prying
* Meddlesome
More specific types of curiosity:
* Intellectual curiosity: Desire to understand things, seek knowledge, ask questions.
* Scientific curiosity: Drive to explore the world around us, discover new things.
* Creative curiosity: Seeking new ways to express oneself, solve problems creatively.
* Social curiosity: Interest in people, their lives, and relationships.
Informal synonyms:
* Nosey parker
* Busybody
* Snooper
The best synonym to use depends on the context and the specific type of curiosity you want to convey.