What a great topic, Matti! As wonderful as museums are, there's nothing like seeing art in the place it was meant to live.
These are all pretty well-known art experiences, but my favorites nevertheless:
El Greco's Burial of the Count of Orgaz, Toledo, Spain -- It's hard to believe this masterpiece is tucked into a side niche of the entryway of a nondescript chapel at the back end of the town. The stark, clean space makes the painting glow even more.
Fra Angelico's Annunciation, Cortona, Italy -- I don't believe it's actually displayed in the space it was painted for, but I count this work as "in situ" because Cortona managed to hold onto this and a few other paintings by its hometown boy. Pretty rare.
Rodin Museum garden, Paris -- Bronze casts of many of Rodin's greatest statues are "planted" in the garden. Walking through this peaceful, green space and coming upon "The Thinker" is a delight. Rodin's figures are so powerful that they seem designed for the outdoors, rather than a claustrophobic museum niche.
Galleria Borghese, Rome -- as you circle Bernini's statues with only a few other visitors, you feel like you're a special guest in the sumptuous villa.
So many many more! Frari Church in Venice, altarpieces in Rothenburg -- I'm interested to see what others think.