Yes as per the new SEBI regulation, even if you are trading only intraday equity, you will need to have a demat account mapped to the trading account.
I guess the logic behind SEBI bringing this is, what happens if a stock hits down circuit and client can’t sell it, where will the stock now be delivered to?
Yeah you should have demat account.
In case of short delivery (read here http://zerodha.com/z-connect/queries/stock-and-fo-queries/consequences-of-short-delivery-nse-bse) the shares will go to your demat account.
So it is mandatory.
In case you are trading only F&O, there is no need of demat account, since F&O settlements are doing within trading account and there is no delivery.