The Vasa Museum in Stockholm, Sweden: The Vasa was a 17th century warship that sank on its maiden voyage--in fact, it never even made it out of the harbor. It was raised in the late 1950s and now sits in its own museum. It's not just the only surviving example of a genuine 17th century ship, although that it pretty amazing. It's the rest of the exhibits: a film about the salvage and restoration, depictions of 17th century life on board a ship and ashore, lessons learned from the restoration process, a wall-mounted exhibit of what the original painted decorations must have looked like, even facial reconstruction and analysis of the skeletons recovered from the ship. I budgeted an hour for the museum, thinking it would be just the ship, but I ended up staying for three.
The Shitamachi Museum in Ueno Park, Tokyo: This is a hands-on museum of everyday life in working class Tokyo before World War II. It consists of mock-ups of shops and homes furnished exactly as they would have been in the old days. That's right down to what would be in the drawers and closets. Small but worthwhile.
The Norwegian Resistance Museum in Oslo, Norway. You have to admire the ingenuity and courage of the people who found ways to bring in news from the outside world or smuggled political activists to the Scottish Shetland Islands, of the teachers who went to Arctic prison camps rather than teach Nazism in the schools, of the pastors who continued to hold services in the woods after their churches were closed for refusing to preach Nazism, and of all the other people who "just said no." The museum even tells about the collaborators.
If you are ever in or near Nara, Japan, in October, don't miss the annual exhibition of the Shosoin treasures at the Nara National Museum. The Shosoin is a wooden storehouse built in the 8th century that somehow creates perfect temperature and humidity for storing all kinds of objects. Every October, a selection of these 1200-year-old objects, including some brought over the Silk Road from as far away as Persia, is taking out for public viewing.
The York Castle Museum in York, England, has nothing to do with the castle, which has long been reduced to a pile of stones. Instead, it's a museum of everyday life in the past. As you enter, there's a series of furnished rooms from various eras, up to the 1950s. There's also a street of typical shops from the past and a collection showing the history of customs connected with birth, marriage, and death. When I went in 2006, the special exhibit was about the history of cleanliness (or uncleanliness in the earliest years).