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Edit: Here is what I had in mind when suggesting the use of the pin change interrupt. Notice that the pin numbers are "hardwired" into the code and cannot be changed easily. This is because:

1. Pins 2 – 7 share a single pin change interrupt request (PCINT2_vect), thus a single ISR is needed to time the six channels.
2. They also share a port (port D), meaning they can all be read by the ISR in a single instruction.

The other possible choices having these nice properties would be pins 8 – 13 (PCINT0_vect, port B) or A0 – A5 (PCINT1_vect, port C).

/*
 * Read 6 PWM signals from an RC receiver.
 *
 * Channels 0-5 are on digital pins 2-7 (i.e. PD2-PD7 = PCINT18-23).
 */
// This always contains the last length measured on each channel.
volatile uint16_t last_pulse_lengths[6];
// Interrupt triggered on every change in pins 2-7.
ISR(PCINT2_vect)
{
 static uint8_t last_pin_states;
 static uint16_t start_times[6]; // start time for each channel
 uint8_t pin_states = PIND >> 2; // shifted to bits 0-5
 uint16_t now = micros();
 // Check every changed bit of the port.
 for (int i = 0; i < 6; i++) {
 uint8_t mask = _BV(i);
 // Record start time on rising edge.
 if ((pin_states & mask) && !(last_pin_states & mask))
 start_times[i] = now;
 // Record pulse length on falling edge.
 if (!(pin_states & mask) && (last_pin_states & mask))
 last_pulse_lengths[i] = now - start_times[i];
 }
 last_pin_states = pin_states;
}
// Return the pulse lengths avoiding race conditions.
static void get_pulse_lengths(uint16_t lengths[6])
{
 for (int i = 0; i < 6; i++) {
 noInterrupts();
 uint16_t tmp = last_pulse_lengths[i];
 interrupts();
 lengths[i] = tmp;
 }
}
void setup()
{
 // Setup the pin change interrupt.
 PCIFR = _BV(PCIF2); // clear pin change interrupt flag
 PCICR = _BV(PCIE2); // enable pin change interrupt
 PCMSK2 = 0xfc; // sense changes on pins 2-7 (i.e. PD2-PD7)
 Serial.begin(9600);
}
void loop()
{
 // Report the pulse lengths on the serial console.
 uint16_t pulse_lengths[6];
 get_pulse_lengths(pulse_lengths);
 for (int i = 0; i < 6; i++) {
 Serial.print(pulse_lengths[i]);
 if (i < 5) Serial.print(", ");
 else Serial.println();
 }
 delay(1000);
}