You may, depending on what country visa you are seeking. There are few European countries that require a person to show proof of insurance as a requirement for a visa grant. For a US visa, there is no such requirement. However, a visa officer may ask depending on each individual case.
In any case, it is wise to travel with travel medical insurance in case of any accidents or emergencies. You will find that it can be quite affordable. Check out pricing, here: Get A Quote
Insurance rates are regulated by law. You can't find the same insurance plan for a lower price anywhere else