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 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).
Other resources for free sound effects and music
- 100 free SFX in Squash & Stretch for Ae
- ccMixter
- Freesound
- Sound Jay
- some (but not all) of the sound effects and music of videvo is free (look for entries in the list which have the text "free" instead of the lightning symbol next to the download button).
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