General Synonyms:
* Timid
* Bashful
* Modest
* Diffident
* Reserved
* Introverted
* Unassuming
* Self-conscious
More Specific Synonyms:
* Cowardly: implies a lack of courage, often in the face of danger.
* Hesitant: implies a reluctance to act or speak.
* Reticent: implies a tendency to be silent or secretive.
* Embarrassed: implies a feeling of awkwardness or shame.
* Inhibited: implies a feeling of being held back or restrained.
* Withdrawn: implies a tendency to avoid social interaction.
The best synonym for shy will depend on the specific context in which you are using it.