Even if you've got travel insurance, there's a good reason to have the EHIC as well.
If you have an accident while abroad, the hospital will treat you and then present you with a bill, which you must pay before leaving the hospital. If you've got an EHIC then there's no problem because your card details will be recorded and the bill will be cancelled. If you've not got an EHIC, you'll have to pay the bill (which might be quite large) and try to claim the money back from your insurer when you return to the UK. (As has been stated, many insurers insist that you carry an EHIC. Quite reasonably, they don't see why they should pay out for treatment which you could have received for free).
One last point: Once you've got an EHIC, remember to carry it with you. It will be of no use at all if you're taken to hospital, after an accident in the street, and your card is still in your hotel room. (You must present the card as soon as you're given a bill. You can't use it to get a refund later).
Chris