Considering that Current Accounts in India give you no interest, why would anyone keep a current account open? Why not just use a Savings Bank Account? ATleast they give you some daily interest on the cash you have with them?
There are restrictions on the number of withdrawals you can make, I think it was around 30 in a quarter where as Current accounts do not have any such restrictions.
There are quite a few other benefits for Companies and Business and it makes sense to open a Current Account rather than savings.
Depending on relationship one can have OverDraft, Statement on Demand, Cheque pick-up, cash pick up and delivery, pooling, and quite a few other benefits. Some of the benefits that were initially available only to Current Account like AT-Par cheque's are now available on savings account from most banks.
For an individual there is very little benefit. The benefits are mainly if one is inot business.