It has been a given for a long time in habitable planet astronomy that only main sequence stars can have habitable planets. Stars spend 90% of their lives on the main sequence, fusing hydrogen to helium at their cores. This is why 90% of stars are main sequence stars. After the main sequence most stars become red giants, baking or swallowing up any planets they have. After the red giant stage very large stars may explode in a supernova, leaving behind a black hole or a neutron star. Smaller red giants lose a lot of mass through a heavy stellar wind and degenerate into white dwarfs. The point is, white dwarfs shouldn't have any rocky planets at all, let alone habitable ones.
But now some scientists (e.g. Fossati et al. 2012) are suggesting that maybe they do--that debris left over from a ruined planetary system may migrate inward to the habitable zone of a white dwarf. What is more, the slowly fading white dwarfs may have a roughly stable luminosity for up to eight billion years, long enough for a planet with water on its surface to evolve life.
Other scientists disagree. Barnes and Heller (2013) point out that A) tidal heating in the tiny (thus close) CHZ of a white dwarf may be severe enough to induce a runaway greenhouse in such a planet, and B) white dwarfs radiate so much ultraviolet light that they may cause water to dissociate in the planetary stratosphere, again leading to water loss.
What is the evidence either way? Of the 4,000 or so confirmed exoplanets as of this date, only one is in a system with a white dwarf, and there is a pulsar in the system, too, and the planet is ten times the mass of Jupiter and 35 AU from the binary (Thorsett et al. 1999). What is more, the system is in the globular cluster M4, and the planet may have formed in a freakish manner involving a close encounter with another star system. No Earth-mass planets of white dwarfs have been discovered, and they may not exist.
So can white dwarfs have habitable planets, or not? I would tend to guess not, but maybe that's only the bias of forty years of main sequence chauvinism speaking. Some day we'll find out.
Barnes, R.; Heller, R. 2013. Habitable planets around white and brown dwarfs: The perils of a cooling primary. Astrobiol. 13, 279-291.
Fossati, L.; Bagnulo, S.; Haswell, C.A.; Patel, M.R.; Busuttil, R.; Kowalski, P.M.; Shulyak, D.V.; Sterzik, M.F. 2012. The habitability and detection of Earth-like planets orbiting cool white dwarfs. Astrophys. J. Lett. 757, L15-L20.
Thorsett, S.E.; Arzoumanian, Z.; Camilo, F.; Lyne, A.G. 1999. The triple pulsar system PSR B1620-26 in M4. Astrophys, J. 523, 763-770.