I am powering a Arduino Uno R3 with 12v using the barrel jack. When measuring with a multimeter, instead of reading 5v from the 5v pins (or any other digital pin for the matter) I see 3.3v; and from the 3.3v pins I read about 2.6 .
If I power the board via USB from my laptop, it all works fine. I'm guessing that this indicates an issue with the 5v regulator; I'd like to know if there can be anything done besides using an external voltage regulator and connecting it to the USB power lines.
I guess the battery in your multimeter is flat.
A cheap DMM could do that without giving you a warning.
As others said, 12volt on the DC socket is in the danger zone, and you can't power much from the Uno at that voltage without overheating the 5volt regulator. A 5volt cellphone charger, connected to the USB socket, is a much better power source. That will bypass the 5volt regulator.
Leo..
If you have 12V available, you might as well use it with a step down. It would save you a space on the AC power strip for the USB charger.
12V is in the range where a relatively small load on the Arduino 5V or pins can produce a lot of heat in the on board regulator. Better to go with a switching supply.