Callie - It could be useful to know where you're travelling to, as requirement differ vastly from EU countries to some in the Middle East. Just an indication would be good.
If you are travelling to the UK, and you have one, please take your EHIC card with you. If you don't have one you can apply here:
https://www.gov.uk/european-health-insurance-card Please do not use any "unofficial" sites, as some try to charge you for the service, which is free.
When I recently had to renew my EHIC card, it arrrived very quickly, so if you don't have one, you might be lucky. The card is for individuals, so if you have companions, they would need their own.
It lasts 5 years, so is worthwhile having anyway.