I can speak for my home town of Stockholm, and here the answer is clearly no. Amsterdam and Copenhagen are a lot more suited for bikers. There have been a handful of improvements in the last 10 years though, and our local politicians sure want to make Stockholms more accessible for cyclists. But we're still lagging quite a way behind. Further, the geography of Stockholm is not as inviting as are the relatively flat geography Copenhagen and Amsterdam. The terrain of Stockholm, especially south of the old town, is quite rugged and hilly.
TL;DR Not very much in Stockholm, but slow progress is being made.
As a Brit living in Stockholm — I can believe that Amsterdam and Copenhagen are better, but Stockholm is still great compared to everywhere else I’ve lived (including several UK and US cities that have reputations of being reasonably bike-friendly). Most roads have cycle lanes, sometimes though not always separated from the main traffic lanes, and there are also quite a few bike-specific trails, integrated well with the normal road network.
thanks- you probably won't see this, but I'm moving there in 2 months... what is cycling like in the winter? Is it possible or just a summer-months activity? I almost always cycle around town in the UK because it gives me independence (as a woman it means I can travel round on my own at night fairly safely), but not sure if it's a viable option in Stockholm when it's winter?
What about Gothenburg! I lived there 6 months, didn't bike myself but bikes were everywhere and all the streets had very clearly marked bike paths, often separated by cobblestone so it's separated by the road.
Bit of a tangent, but when my aunt and cousin were visiting, we were on the spårvagn and I looked out the window, a tjej was riding a bike, holding a bag of strawberries, and it was raining. I said "That! That right there is Sweden." I don't think they appreciated that moment nearly as much as I did.