Can your H1 Visa be transfered from one company to other.

I have my H1 B visa, done by my current company. I have not travelled from my current company till now even once. I am planning to switch. Can i have my visa transfered to new company?

Is there some restriction that i need to travel once through the company who worked on my visa?

The new employer will have to file a cap-exempt petition (loosely referred as H-1 transfer). Once approved, you will have to appear for visa stamping (if the current visa stamp has expired or current employer gets it canceled as part of your exit process). Then, you can travel to US w/ new petition and old/new visa stamp (depending upon the case).