It is in the soul of a human to strive for places that are closed and not accessible. Open Garden days in Amsterdam is a chance to fulfill some dreams - The Open Garden Days Amsterdam is an annual in the 3rd weekend of June. Organized by the Canal Museums, it is a 3 day long event in which 30 privately kept splendid canal house gardens are open to the public. Although you have to buy a ticket for enter gardens, we still included the event in our list due to its special value.
National Geographic has included tram Nr. 2 ride in Amsterdam within top 10 trolley rides in the world. The Nr. 2 tram travels along many of Amsterdam’s major tourist attractions, such as the Royal Palace, De Nieuwe Kerk (New Church), Begijnhof, Bloemenmarkt (flower market), Rijksmuseum, Van Gogh Museum, and Vondelpark. Not absolutely for free, but good value for a tram ticket purchased.
I amsterdam card gives you free entrance to all major museums and activities in Amsterdam, including Van Gogh Museum and Hermitage Amsterdam. As major museums in Amsterdam don't offer any free entrance days or hours this card makes a true value for active traveller.