This will allow full RGB control of an RGB LED (aprox. 1.6 million colours). This is merely a proof of concept; real applications might be to connect and RGB LED srtip for lighting your room or your PC.

Parts list:

Arduino UNO Rev3
RGB LED (or RGB LED strip / other RGB display)
IR remote & receiver
3 220R resistors
Prototyping board (I used a prototyping shield as well)
6 jumper cables

Here I use the bottom two rows of digits on my remote (4-9) to control the intensity of each colour.

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Step 1: Wiring

You may need to play around with the pins used. I had to change mine until I found some that work. I think there is a bug with the IR library I used; I will need to experiment more with this.

Step 2: Code

First, you will need to install the IR library: https://github.com/z3t0/Arduino-IRremote

Find the code here: https://gist.github.com/Marcel-Robitaille/bebb855812428b19bb2c

You may need to change the codes depending on your remote.

#include <./IRremote.h>

int pinR = 9;
int pinG = 6;
int pinB = 5;
int pinSignal = 11;
IRrecv irrecv(pinSignal);
decode_results results;
long codes[6]= {
	0xFD28D7,	//4
	0xFD18E7,	//7
	0xFDA857,	//5
	0xFD9867,	//8
	0xFD6897,	//6
	0xFD58A7	//9
};
int valR = 0;
int valG = 0;
int valB = 0;
void setup(){
	Serial.begin(9600);
	irrecv.enableIRIn();
	pinMode(pinR, OUTPUT);
	pinMode(pinG, OUTPUT);
	pinMode(pinB, OUTPUT);
}
void loop(){
	if(irrecv.decode(&results)){
		if(results.value == codes[0] && valR < 255){
			valR++;
		}
		else if(results.value == codes[1] && valR > 0){
			valR--;
		}
		else if(results.value == codes[2] && valG < 255){
			valG++;
		}
		else if(results.value == codes[3] && valG > 0){
			valG--;
		}
		else if(results.value == codes[4] && valB < 255){
			valB++;
		}
		else if(results.value == codes[5] && valB > 0){
			valB--;
		}
		display(valR, valG, valB);
		Serial.print("Red: ");
		Serial.println(valR);
		Serial.print("Green: ");
		Serial.println(valG);
		Serial.print("Blue: ");
		Serial.println(valB);
		Serial.println("");
		irrecv.resume();
	}
}
void display(int red, int green, int blue){
	analogWrite(pinR, constrain(red, 0, 255));
	analogWrite(pinG, constrain(green, 0, 255));
	analogWrite(pinB, constrain(blue, 0, 255));
}