It is strongly advised to have Health Insurance on your own as well because of reasons of continuity. Firstly, if you change your job, you might not necessarily get Health Insurance from your new employer. In any case you will be exposed to health costs in the transition period between jobs.
Secondly, the track record that you have built in Health Insurance at your old employer will not transfer to the new company policy. Covering pre-existing diseases will be a problem in most group insurance policies.
In the recent years, many employers are mandating employees to share a part of the Health Insurance premium and claim amount (copayments) in order to prevent frivolous and fraudulent claims.
Therefore to avoid the above problems, it is advisable to take a private policy in addition to your company provided group Health Insurance Policy.