My first CD was a gift for Christmas and was Weird Al Yankovik's Greatest Hits album. Its a good CD but most of his classic stuff from the 80s.

The first CD I bought for myself was Pioneer's Anime division releasing a CD with the translated opening and ending themes to several of their big anime series like Tenchi Muyo!, El Hazard, and The Hakkeden. I love this CD and its incredibly rare now. Especially since it contained rare tracks like the ending theme to Green Legend Ran:



Now to show how much of an old fogey I am, my first cassette tape just ask your parents what it is I bought for myself was Billy Joel's River of Dream album.