On that specific project it was right on a prototyping shield. However in another project using Phidgets(before I discovered NerdKits, arduino and netduino etc.) I ran one ~ six feet from the controller using some cat5 wire I had handy. The LM34 data sheet has some notes about length of the wire and some additional discreet component circuits. My application worked fine with the sensor soldered to the end of the wire.
Check out this article: "The Long Arm of the Nerdkit" This guy went thirty feet.
I've got a Dallas DS18B20 programmable resolution 1-wire digital thermometer sensor sitting on my bench just itching to be experimented on. Multiple addressable sensors on the same wire. This device does not suffer from analog noise interference as the LM34 may experience. I believe fifty meters wire length is not unheard of with the DS18B20. (see this discussion)
c ya.. - jeffa