I believe you might be referring to Tomtit: http://www.tomtit.se/english/
There's a similar sort of thing that I've been to in Cardiff, the UK, called "Techniquest": http://www.techniquest.org/start/
I've also been to At-Bristol in Bristol, the UK: http://www.at-bristol.org.uk/
I found the following page too which is a list of interactive science centers around the world, I have no idea if it's comprehensive or not: http://www.cs.cmu.edu/~mwm/sci.html
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Children, discovering and learning about the world around us at The Natural History Museum and Tom Tits (Södertälje).
Exhibits explain the wonders of physics, biology and other sciences.
Both are technical Museums.
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Are there any analogs of such museum in other European countries?
In Paris, there are two of them: Palais de la découverte Cité des sciences
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Also - Tekniska Museet has an interactive part called Teknorama with lots of fun and learning things to do.
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Another museum that might be interesting for kids (and adults as well) in Stockholm is Skansen (the open air museum).
It recreates the way of life in rural Sweden 200 years ago.
Various traditionally dressed craftsmen show their crafts in old historical cabins with historical decor.
Crafts widely range:
glass-blowing, making cheese, baking, making yarn out of flax, etc.
All these processes are demonstrated and explained, and children are able to participate (there might be a line to participate, but it's possible to watch).
The bakery sells their pastries directly to the customers, and I was told that the cheese made in Skansen is used in the food that is served in their cafeteria.
In addition there is also a zoo in Skansen.
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Are there any analogs of such museum in other European countries?
I can recommend Technorama in Winterthur, Switzerland.
It is a technology museum with various experiments suited for children but also all other age groupes.
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I heard about museum near the Stockholm in which children can make some experiments in chemistry, physics and so on, but I completely forgot its name. Can you help me to find some information about it (in English, if available)? Are there any analogs of such museum in other European countries?
Are there any museums in Stockholm for children? (not Junibacken)
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The musueum you are referring to may be The Natural History Museum and Tom Tits (Södertälje), and there are similar museums in Cardiff (Techniquest), Paris (Palais de la découverte  Cité des sciences). Another interesting open air museum for kids in Stockholm is called Skansen. The Museum referred to could be Tomtit:  http://www.tomtit.se/english/ . However, there are similar Museums like  "Techniquest"(Cardiff, the Uk:  http://www.techniquest.org/start/ ,  Children, discovering and learning about the world around us at The Natural History Museum and Tom Tits (Södertälje), Palais de la découverte  Cité des sciences (Paris)  Skansen  (the open air museum) in Stockholm.
The Museum you are referring to could be Tomtit:  http://www.tomtit.se/english/   Similar museums are   "Techniquest"(Cardiff, the Uk:  http://www.techniquest.org/start/ ,  Children, discovering and learning about the world around us at The Natural History Museum and Tom Tits (Södertälje), Palais de la découverte  Cité des sciences (Paris)  Skansen  (the open air museum) in Stockholm.