To use a boot animation, your device must be rooted. I won't go into the specifics of that here, as there are countless tutorials for it online. Once you have root access, simply replace bootanimation.zip located in /system/media/ (for Android 4.x at least) with one you take from the list below. Reboot your phone, and the animation appears. It's that simple!
Note that the downloads below are zipfiles that contain the zipfiles you'll copy to your phone. The file you need is called bootanimation.zip and you mustn't rename it, as your system will specifically search for a file with that name.
The examples below have been compressed (reduced size, colour and framerate) to load faster; the actual animations are 720 by 1280 pixels and look far better. All were adapted from the work of others, so I provide links to the original creators when possible.
|The ultimate trip
2001: A Space Odyssey. The full sequence.