I couldn't be more wrong.
It turned out I couldn't get a wifi connection, because bluetooth was disabled using that small GNOME Bluetooth indicator. While bluetooth was disabled, my wifi card was able to list networks and NetworkManager could try connecting to one, however, it never succeeded. dmesg spit out some messages like "
direct probe to (access point MAC address) timed out" and after some time even "iwlagn 0000:03:00.0: Microcode SW error detected. Restarting 0x2000000.".Thanks to Zander Hill's comment in my bug report #663298, I found out that by enabling bluetooth, I could connect to wifi networks again with no problems.
So if You ever run into connectivity problems, feel free to try out everything completely unrelated to Your wifi card just to be sure.