In my mind... I would say that the role of a Dancer is "
Support". They aren't quite capable of being a Main Healer except in some circumstances.
They also can fill the following additional roles:
Puller
Backup Healer
Hate Control / Hate Assist
From
http://wiki.ffxiclopedia.org/wiki/Party#Basic_Strategy
Support: "Member of the party that facilitates the functions of a party. Able to increase the effectiveness of all other members of the party by enhancing the ability to deal damage, tank, and/or directly reduce downtime through usage of abilities that restore MP. The role of a support character is quite simply to support the other members of the party. While not having a direct impact on the goals of the party, a support character is just as important as the rest of the party. Having a support character around makes everybody's job easier - as one can easily enfeeble an enemy to deal less or take more damage, directly enhance a damage dealer's damage potential, or provide a safety cushion for healing when the healer has exhausted his/her resources."
So to answer your question... DNC can replace the following jobs: RDM, BRD, SMN, COR