While After Effects itself does not contain any stock music or sound effects, the Creative Suite or Creative Cloud has a big library of stock music and sound effects included.
Music and Sound Effects in CS4, CS5 and CS5.5
In CS4, CS5 and CS5.5 the audio files are conveniently accessible from Adobe Soundbooth as shown in Andrew Davis' tutorial Free Music & Sound FX in Soundbooth.
Music and Sound Effects in CS6 and CC
In CS6 and newer versions you have to open Adobe Audition and open the menu entry "Help->Download Sound Effects and more" to download more than 30GB of royalty free sounds, scores, music loops and music beds (you have to register but its free).