Do debit cards need to have a chip to work in Europe?

Debit cards without chips work fine. Credit cards without chips work also if they are used in transactions where the card is swiped. You may have heard that cards without chips will not work but that refers to credit cards and that is usually in a situation in which there is no person-to-person interaction and thus no ability to swipe the card.

I not know about using them for purchases, but for use in ATMs no chip is required. We spent 30 days in Italy and used our non-chip debit card in several ATMs and never had a problem.

These cards can be used for purchases.
The machine will always be brought to your table, or will be on the counter in front of you.

The vendor swipes the card and you sign a copy of the receipt, he keeps the other one.
There is no "tip line" - if you want to leave a tip, you do that in cash.

Not usually, but there are some cases where a card without a chip may not work, for example at self-service gas stations or some other automated payment terminals, where it may not be possible to swipe a card. I've had trouble refueling in France a few years ago because of that, back in the day when my bank wasn't issuing chip cards. It didn't help that I had a PIN code, the machine simply couldn't read my debit card.

They don't need a chip to work in an ATM. Purchases may be different, unlike non-chip credit cards, which continue to work pretty much everywhere in a face to face transaction; except possibly in certain countries.

It depends on what you are trying to do. Magnetic swipes work fine at ATMs and most larger retail businesses and restaurants. Where you may have trouble is automated ticket machines, some toll road stations, and many grocery stores. I have found that some of these vary by country though. If you share where you are traveling some of us may have recent, specific experience!

I spent June in London and in Portugal with debit card and credit card both without a chip and they both worked fine the whole time I was there. I see that vannjonni thinks she heard that..... I wonder if she imagined that and if she actually heard that, where she heard that. A common post on this site. Happy travels.