A modification of ColorCrossFader from the Arduino Playground to work with Adafruit NeoPixels. This script is using a 7 pixel strip. Adjust the #define to suit.

NeoPixelFade

#include <Streaming.h>
#include <Adafruit_NeoPixel.h>

#define BAUD 9600
#define LEDPIN 9

long pMillis = 0;
long interval = 5;
int fadeCallback = 0;

uint8_t 
    rVal = 0, 
    gVal = 0, 
    bVal = 0;

Adafruit_NeoPixel LED = Adafruit_NeoPixel(1, LEDPIN, NEO_GRB + NEO_KHZ800);

void setup() {
    Serial.begin(BAUD);
    LED.begin();
    LED.setPixelColor(0, LED.Color(rVal, gVal, bVal));
    LED.show();
}

void loop() {
    switch (fadeCallback) {
        case 0: fade(interval, 255, 0, 0, 1); break;
        case 1: fade(interval, 0, 255, 0, 2); break;
        case 2: fade(interval, 0, 0, 255, 3); break;
    }
}

void fade(int duration, int toR, int toG, int toB, int cb) {
    for (int i = 256; i > 0; i--) {
        unsigned long cMillis = millis();
        if (cMillis - pMillis > duration) {
            pMillis = cMillis;
            
            rVal += (rVal < toR) ? 1 : (rVal > toR) ? -1 : 0;
            gVal += (gVal < toG) ? 1 : (gVal > toG) ? -1 : 0;
            bVal += (bVal < toB) ? 1 : (bVal > toB) ? -1 : 0;

            if (rVal == toR && gVal == toG && bVal == toB) {
                fadeCallback = cb;
            } else {
                for (int j = 0; j < LED.numPixels(); j++) {
                    LED.setPixelColor(j, LED.Color(rVal, gVal, bVal));
                }
                LED.show();
                
                Serial << "R: " << rVal << "|" << toR << ", G: " << gVal << "|" << toG << ", B: " << bVal << "|" << toB << endl;
            }
        }
    }
}