Contributed by: Smokey D Dope

They can not.
Blacklights do not produce the correct spectrum of light to grow plants.

The only lights that currently produce the required color spectrum of light to grow plants are the following;

Suitable for Growing:

Flourescent (Tube shaped)

Compact Fluorescent
(a flourescent tube with ballast included that screws into regular light fixture)

Metal Halide (MH) Best for Vegetative growth, but it doesn't contain all of the spectrum needed later during flowering for truly outstanding buds. the light shines a blueish/white color

High Pressure Sodium (HPS) Best for Flowering. Ok for Vegetative. shines a yellow/orange color. All can be purchased at your local home/lumber store.

Not suitable for growing:

Blacklight type flourescent lights.

ANY incandescent lamp
(if it screws into a regular lamp, it won't produce worthwhile buds). Exception, compact flouro mentioned above)

Halogen

Mercury Vapor