Yes, because it could cover you (depnding on where you are going) for minor mishaps without having to go through all the hassle involved in an insurance claim.
Just an additional point:
It's no use having an EHIC if you've not got it with you when you arrive at a hospital.
For example, if you fall and break your wrist, the local casualty unit will put it in a pot and then present you with a bill, which must be paid before you leave the hospital. If you show them your EHIC that bill will be waived but that won't be possible if you've left the card in your hotel room. ALWAYS CARRY IT WITH YOU (e.g. in your wallet or purse).