Acording to the datasheet for the sensor you need the resistor. It's there to protect the sensor from being damaged by too much current. Removing it will cause to much current to go through the sensor and fry it.
If everything was working you should get numbers in the serial monitor between 0 and 1023. 0 = 0V on the analog pin 1023 = 5V on the analog pin. Depending on the value of the resistor and the temperatrure you are sensing you might get values that do not cover the entire 0 - 1023 interval.
If the sensor got very hot, it's likely that it is damaged.
The analog in pins are connected to a AD (Analog to Digital) converter in the Atmega processor. It will convert a voltage in the range 0V - 5V to a 10 bit value, i.e. a number in the 0 - 1023 range.
Hope this helps a bit.