Although you might find the concept of playing music specifically for your parakeet rather silly, pet birds and music are hardly a mismatch. Birds sing, don't they? And some parrots are actually fans of human music as well.
Parakeets, like many other pet birds, often react fondly to music that is serene, peaceful and quiet. Loud music is a no-no for them. Two genres that might put your parakeet's mind at ease are soft classical and New Age music. Whether you opt for the lilting sounds of Irish chanteuse Enya or the tranquility of Chopin, there's a good chance that you'll engage your parakeet, all the while making him feel comfy and happy. Some parakeets even adore Celtic music. Keep thrashing heavy metal and repetitive, rapid dance music at bay, however. Not only can the right music be helpful for overall positive feelings, it also can be useful for covering up sounds that might scare your parakeet—think persistent outdoor construction.
Your parakeet might also greatly appreciate nature sounds. The "music" you play for him doesn't necessarily have to be melodic, just easy on the ears. The sounds of lightly falling rain, waves, waterfalls and flowing rivers might all be effective for making your parakeet feel good. Just make sure never to play a piece that features any predator calls!
Although it's not necessarily serene, many pet birds also have fun listening to pop songs straight from the radio. A lot of them are especially partial to music that features vocals, and some enjoy just listening to people talk. Remember, too, that although many birds react well to certain types of music, all birds are individuals with their own tastes and preferences, just like people. Try different radio stations to see what your pet responds to. You may find you have common tastes.
You might even be able to "condition" your parakeet to appreciate certain types of music. In these situations, opt for something placid. Wait around for your parakeet's happiest and most content times and then promptly turn the music on. Do this on several different occasions and voila: positive association to the music firmly established. It also helps to do this right before your bird goes to sleep every night—a key peaceful time for him.