Powering servos with external source
Most likely you fried the voltage regulator or the diode on your Arduino board (depending in which power source you used), because the servo has drawn too much current.

Many Arduino Kits or Starter Packs come with really small servos. These do not need much power (especially when no mechanical load is attached to them), so you can power them directly from the 5V pin. Greater/stronger Servos draw much more current and cannot be safely run in the 5V pin.

Many tutorials show this, because it is an easy start for a beginner. And with the right servo it works. More sophisticated cases are not covered there.

EDIT:

Since your Arduino works fine, the voltage regulator and/or the diode should be fine. I tested the Knob example on my Arduino Nano, while powering the servo on the Arduinos 5V pin (and the Arduino is powered over USB). When the Servo is moving, you can see that there is a significant power draw (The power LED gets a bit dimmer), but not so much, that it would be a problem for the Arduino or USB port. Also the example code works as it should, without the servo heating up. I also used a SG90 Micro Servo (9g, by Tower Pro; same as in the tutorial you linked). I also tried the same with an external power source (5V from a powerful USB charger). It still works as intended, but with more power, since the servo now can draw much more current to produce a higher thrust.

So the only thing, I can think of for your problem is, that you either have corrupt hardware, or you have connected it wrong (for example wrong polarity). My Servo has the same color coding for the wires as in the tutorial you linked. Brown is ground, Red is 5V Vcc and Yellow is for the pulse signal.