I went to the Uber site but could find no actual list of locations. Can one use Uber, Lyft, or Cabify (we got that one in Spain) in Copenhagen? Oslo? Bergen? or Stockholm? thanks

Last I heard, Uber was banned in Copenhagen, no idea if that situation has changed.
Uber is available in Stockholm AKAIK but I would be careful using it or any other taxi service in Sweden, since taxi drivers are well known for ripping people off. I use an app called Taxi Kurir for taxis in Sweden, it's worked quite well for the rare occasions I need a taxi.

Uber is banned in Norway.

I know that Uber does not operate in Norway. I don't have any first-hand knowledge of Sweden or Denmark, but I think Uber operates in Sweden (at least in Stockholm and Gothenburg). However, taxis are extremely expensive (significantly more so than the very good public transportation) and rates can vary depending on the company you use (some have fixed prices, some not). I know Americans like their convenience, but a couple of $50 taxi rides may teach you to appreciate public transport.

Lyft is only available in the US and Canada, while cabify is available in South America, Spain and Portugal. Uber's site still claims it operates in countries where it doesn't and it's not clear whether it does operate outside of Oslo. Indeed, it's not clear whether it operates in Oslo.

With all the controversy surrounding Uber, I think I'd prefer to get a properly licensed cab with a meter.

Catch public transport, it is cheap clean safe and puntual why do you want to shed any of those benefits for worse things at a higher price?

This is why

a quieter, gentler trip to Scandinavia

Thanks all, and yes, thanks Odin for understanding why we may need taxis. If we can we will use the public transport. I think we've gotten a bit spoiled by the ease of uber and lyft here in the US, although yes, the controversies are worrisome. In our small town uber always tells us that the nearest car is 200 miles away! lol

Don't throw shade on all "Americans" about this, I always use public transporation when possible in any city, and I don't use Uber ever. This is an individual issue about people who are spoiled and don't care about the environment.