During the Credits
There are no extras during the credits of The Lord of the Rings: The Fellowship of the Ring.
After the Credits
There is no stinger after the credits of The Lord of the Rings: The Fellowship of the Ring.
In the Extended Edition, the credits are longer because they include additional credits and the official LotR fan club credits. The fan club credits in TFOTR covers all the yearly charter members that paid either the one-year for this film, two for the first two films or three year membership for all three films. Several cast members are also included in the fan club credits.