I found three free Wi-Fi networks in Stockholm. One was an independent cafe, Café Edenborg, where there is both open Wi-Fi access and available power points for those battery recharge moments. The coffee was good too.
The next one was in a local burger chain called Max. I saw two Max locations during my stay, but could only detect Wi-Fi in one of them. The one where the Wi-Fi was present did have a sticker on the door though indicating that WLAN was available. At that location, the connection was open to the internet without any need to sign in, or even accept terms & conditions.
Finally, the most common of the free networks I found was SkypeZones. These free networks, which appear to be sponsored by Skype, are all over the city. They provide reasonably good strength outside on the street, and two networks: SkypeZones and SkypeZones_Phones. As with the other two networks, they are entirely open – no sign in page or terms and conditions page at all. I was able to surf the web, make Skype calls and even make SIP calls through VoiceStick at a number of these locations with no problem at all.