What is the sampling-rate of the `analogRead()`? I am about to Fourier analyse some data I've taken, but i need to know at which sampling rate the data was written to the serial monitor. I've found a lot of threads about how to increase it and such but not a single one that lays down some information about what the sampling-rate is. 

My code is very simple, here it is: 

      // the setup routine runs once when you press reset:
  void setup() {
    // initialize serial communication at 9600 bits per second:
    Serial.begin(9600);
  }

  // the loop routine runs over and over again forever:
  void loop() {
    // read the input on analog pin 0:
    int sensorValue = analogRead(A0);
    // print out the value you read:
    Serial.println(sensorValue);
  }
The ADC in default configuration will take 104 µs to make a sample (which agrees with Edgar Bonet's comment of roughly 9600 per second).

You can speed that up somewhat by changing the ADC prescaler from the default of 128. See ADC conversion on the Arduino (analogRead). A prescaler of 32 will reduce that to 26 µs and still give quite acceptable results.

You can also run the ADC asynchronously (in the background) so you can transmit the previous result while obtaining the next one. A higher baud rate than 9600 baud would be highly recommended in this case.

People have been doing FFT analysis using the Arduino Uno and similar. I suggest you Google for relevant posts about that.