Digital gates are great for switching LEDs on or off. Micro-controllers are even better and so are single board computers. That is because they contain several gates to control the LEDs. To top it all, you can program single board computers such as the RBPi or Raspberry Pi to control several LEDs individually to run at different on/off cycles. Additionally, multiple color LEDs are available, such as RGB LEDs, with which you can generate any combination of the basic red, green and blue colors.
Although the GPIO pins of the RBPi can switch on an LED, the pins cannot supply beyond their limit. Therefore, when driving LEDs from the GPIO pins, a current limiting resistor is necessary in series with the LED, to prevent the IO pin from being damaged. The resistance value will depend on how much current the IO pin can source or sink, and the supply voltage of the RBPi or LED.
The RBPi has a 40-pin GPIO header among which, you can control several pins through software. The most common use of external circuits and LEDs with GPIO pins is to indicate status visually. For example, you may be controlling a remote circuit with software, and an LED nearby can indicate its status. The LED lights up to indicate the remote circuit is powered.
It is a good thing that human eyes have something called the persistence of vision. When we see something, its image persists in our eyes for a brief time. Therefore, we can see flashing lights only when they are flashing relatively slowly. Beyond a certain speed, our eyes cannot make out the individual flashes and the flashing light looks as if it is steadily lit. Using a technique called PWM or Pulse-Width Modulation, and controlling the on time of a GPIO pin through software, we can make an RBPi drive an LED such that it looks as if the LED is breathing. Doing the same with an RGB LED, the RBPi can cycle the lights to produce any color in the rainbow.
You can build a simple RGB LED board with a single bright RGB LED, three current limiting resisters and a four-pin connector on a prototype PCB. RGB LEDs have four pins and come in two configurations, common cathode and common anode. In the common cathode configuration, the package combines the cathodes of all the three LEDs into a single pin with the anodes individually available. For the common anode configuration, all the three anodes are combined into one pin, while the cathodes are individually accessible.
To drive an RGB LED you will need to connect its individual anodes or cathodes to three GPIO pins through current limiting resistors. If you use a common anode RGB LED, you will have to connect its common anode to a supply voltage. For a common cathode RGB LED, you will need to ground its common cathode. Now, you can switch on an individual LED of the combination by switching on the corresponding IO pin. See this tutorial for writing simple Python scripts for controlling the LEDs via the RBPi.