Exploring the world of art has never been more accessible, with numerous museums across the world. Several European art museums offer free admission to their permanent collections. Keep in mind that some museums may have specific days or times when entry is free.

• The British Museum provides free entry to its permanent collections, allowing visitors to explore a vast array of historical artefacts.
• The Louvre offers free admission to its permanent collections on the first Friday of each month after 6 pm, except for August and July.
• Entry to the Vatican Museums is free on the last Sunday of each month from 9 am to 2 pm, with final entry at 12:30 pm. However, it's important to note that the museums can get very crowded on these days.
• The National Gallery in London offers free entry to its permanent collection, featuring works by renowned artists such as Leonardo da Vinci, Vincent van Gogh, and more.
• The Prado Museum provides free access to its permanent collection from Monday to Saturday, 6:00 PM to 8:00 PM, and on Sundays and holidays from 5 pm to 7 pm.
• The Moderna Museet in Stockholm has free admission on Fridays from 6 pm to 8 pm. 
• The Reina Sofia Museum in Madrid offers free admission during certain hours, typically in the evenings. The free admission hours are on Monday, Wednesday, Thursday, Friday and Saturday from 7 pm to 9 pm and Sunday from 12:30 pm to 2:30 pm.

Always check the official websites of museums for the latest information on admission policies and free-entry days. Keep in mind that special exhibitions or events within these museums may still require a separate ticket.