Scandinavia is generally considered very safe, so you usually don’t need to behave much differently than you would at home. The main risks are the same as anywhere: theft in the wrong area, loss, or damage.

Practical precautions:

• Use normal street awareness and avoid obviously unsafe neighborhoods, especially with expensive gear on display.
• A good bag and secure strap are worthwhile.
• Focus on preventing loss of photos as much as loss of gear: back up your images regularly.
• Put identification on or in your gear, such as a contact photo on the memory card and a name/address label inside the bag, to improve the chance of recovery if lost.

In short: don’t be overly worried about carrying a camera in Scandinavia, but use the same common sense you would in any unfamiliar city. Protect your images with backups, and organize your gear so it’s secure and identifiable.