There are several types of corkers available.  We highly recommend a floor corker with jaws that compress the cork prior to plunging it into the neck of the bottle. Other corkers (twin lever, single lever, and compression corkers) rely on human muscles to compress the cork and push it into the bottles.  

Floor corkers, while more expensive, use simple levers and mechanical advantage to carefully compress the corks and insert them precisely into the bottles without damaging the cork  Also, they hold the bottles steady in a spring-loaded base. They are really worth the extra money.