As a noun:
* Vault: This is a very close synonym, especially for a curved structure.
* Curve: A more general term for any curved shape.
* Bridge: When referring to a specific type of arch that crosses over a space.
* Span: Used to describe the distance an arch covers.
* Concave: Refers to the inward curve of the arch.
* Arcuate: A formal term for something having the shape of an arch.
As a verb:
* Curve: To bend into a curved shape.
* Vault: To move or pass under an arch or curve.
* Span: To extend over a space.
* Bridge: To connect two points by building a bridge.
Other related words:
* Arched: Adjective form of "arch."
* Arcuated: Adjective form of "arcuate."
* Curved: Adjective form of "curve."
* Curvature: The state of being curved.
The best synonym for "arch" will depend on the specific context and the meaning you want to convey.