General:
* Level
* Flat
* Parallel to the horizon
* Across
* Lateral
* Transverse
More specific:
* Recumbent (lying down)
* Prone (lying face down)
* Supine (lying face up)
* Reclining (leaning back)
* Parallel (specifically when referring to lines or surfaces)
The best synonym will depend on the specific meaning you want to convey.