ADC register always returning high
First, let me give a couple of suggestions on the programming style.
There is no point in defining your own variables for accessing the
hardware registers: the avr-libc does that for you, you just have to
#include &lt;avr/io.h&gt;. Actually, you don't have to #include anything:
the Arduino IDE automatically #includes Arduino.h, which in turn
#includes avr/io.h.

Next, the same avr-libc also defines macros for the bit names, so you
don't have to explicitly write binary numbers in your own code (which is
error-prone). And a couple of utility macros that you can use to make
the code a little bit more readable. For example:

void adc_init()
{
    ADMUX  = _BV(REFS0);  // ADC reference = AVCC
    ADCSRA = _BV(ADEN)    // enable the ADC
           | _BV(ADPS2)   // set prescaler to 128
           | _BV(ADPS1)   // ditto
           | _BV(ADPS0);  // ditto
}

unsigned int adc_read(unsigned char adc_channel)
{
    ADMUX   = _BV(REFS0) | (adc_channel &amp; 7);  // select channel
    ADCSRA |= _BV(ADSC);  // start conversion

    // Conversion is complete when ADSC goes low.
    loop_until_bit_is_clear(ADCSRA, ADSC);

    return ADC;  // return the adc data register
}


Now, let's answer your actual question. When you set both REFS0 and
REFS1 to 0, the voltage reference is stated to be “AREF, internal V
REF turned off”. The implication is that you are supposed to bring your
own voltage reference and connect it to the AREF pin. Otherwise AREF is
left as a floating input. This is illustrated in the schematic of the
ADC. Here is the relevant part:



As you see here, REFS0 is used to connect AREF to one of the other
possible references: either AVCC or the internal bandgap. If REFS0 is
zero, the transistor depicted above is off, and AREF is left floating.