There are several kinds of travel-related insurance, sometimes sold as a package, sometimes separately:
- Travel health insurance: Covers healthcare costs if you have an accident or fall ill during a trip abroad. This type of insurance is mandatory to get a Schengen visa (but if you reside in a Schengen country or are otherwise exempt from the visa requirement, that's moot) and it's possibly the most important one, because something like an hospital stay can become very costly very quickly.
- Cancellation: Covers the costs of non-refundable tickets you already bought if you are forced to cancel a trip (typically for a limited number of reasons out of your control, like a disease, the death of a close family member, losing your job, etc.)
- Repatriation: Covers the cost for (medicalized) transportation back to your country of residence if you have an accident or contract a disease abroad.
- Luggage damage or theft: Covers some costs (sometimes also with some assistance and/or emergency funds) if your luggage is damaged or your ID, credit cards, etc. are stolen.
- Liability: Covers legal fees and damages you might have to pay if someone brings a lawsuit against you for something you have done during your trip.
- Interruption: You get a bit of cash if you are forced to interrupt a trip (again for specific reasons like losing a family member) and therefore lose the benefit of any arrangements you made and/or need to buy a new ticket on short notice.
- Life: Your family gets a lump sum if you die during the trip.
- Rental car: Covers the bits that are not covered by the basic rental insurance (i.e. excess in case of accident, theft).
- Mountain/wilderness search and rescue assistance. Even a minor injury in a remote place can leave you with a bill in the thousands of euros for helicopter assistance (you can also buy an insurance against this separately from ski resorts or alpine clubs, incidentally).
The first one is probably less useful for you, if you are covered through the “European Health Insurance Card” (EHIC) system. Some details are a little complex but it would for example pay for hospitalization elsewhere in the EU. Depending on local rules, some costs might not be fully covered and an additional medical emergency/health insurance could make sense to cover the difference but it should at least avoid any catastrophic medical bill. If you don't already have an EHIC, check with the local insurer/social security administration if you are eligible and carry it with you.
Others (like the liability insurance or insurance against theft) are possibly already included in some other insurance contract you have (e.g. in France, it's common to have a generic liability insurance as part of a home insurance package) or through a premium credit card (e.g. repatriation or cancellation might be covered if you use the card to pay for the tickets).
In all cases, it's difficult to decide for you if it's “necessary”. In some countries, liability or legal insurance is very common, in others not so much. As long as nothing happens, you don't notice it but if you are faced with a huge liability, you are of course happy to have it. The whole point of insurance is that such events are not very common but can be very costly when they do happen.
But for the smallest items mentioned above (say luggage), you can also put some money aside and consider yourself self-insured. Insurers know more than you about the risks, want to make a profit and set prices accordingly. Since luggage does not cost so much and there is typically a rather low cap on claims, you can easily know what the “worse case scenario” is and decide that you have enough money to face these costs on your own.