Re: Can hermaphrodites impregnate themselves

In short: 
Yes, they can but it is rare. In nature where hermaphroditism is the norm, 
there are mechanisms in place, that make it very unlikely that self-
fertilization occurs. 

In more detail:
The term is derived from the legend of Hermaphroditus.
A heraphrodite is an organism that has both male and female sex organs. 
Hermaphroditism is the norm in such species as earthworms and snails, and is 
common in flowering plants. 

Central point in sexual reproduction is the union of two gametes (sex cells, 
often called egg and sperm) to produce a zygote, which combines the genetic 
material contributed by each parent. 

In self-fertilization the male and female gametes come from the same 
organism; in cross-fertilization they come from different organisms. 

Monoclinous plants have hermaphrodite, or perfect, flowers, each of which 
has both male and female elements (stamens and carpels); monoecious plants 
have flowers containing only male elements and others containing only female 
elements, both occurring on the same plant. Only a few flowering plants are 
dioecious, that is, carrying male and female organs on different plants. 
Most hermaphroditic plants produce male and female elements at different 
times to ensure cross-pollination; a few, such as the violet and the evening 
primrose, are habitually self-pollinated.

Self-fertilization very rarely occurs in animals; the norm is that even 
hermaphrodite animals cross-fertilize each other, with the parents 
functioning as male and female simultaneously, or as one or the other sex at 
different stages in their development. In most cases the spermatozoa and ova 
mature at different times (successive hermaphroditism), or the male
and female external organs are located so that self-fertilization is 
impossible. Among the invertebrates, sponges, coelenterates, some mollusks, 
and earthworms are regularly hermaphroditic.

Flatworms (planaria) have a complete set of male and female gonads in each 
segment and regularly fertilize themselves. Self fertilization habitually 
occurs in a smaller number of invertebrate animals, in the hagfish and 
tunicate, and in the sea bass of the genus Serranus. It occurs occasionally 
in other fishes, in frogs, toads, and certain newts among the amphibians.

True functional hermaphroditism is rare or absent in higher animals and 
humans. One occasionally sees animals called hermaphrodites that appear 
intermediate in form between males and females, but such animals are usually 
sterile, and, when fertile, do not produce both fertile eggs and fertile 
sperm. Such organisms are often called intersexes or sex-intergrades; 
intersexes in the fruit fly have been shown to arise from inheritance of an 
abnormal ratio of male Y chromosomes to female X chromosomes. 

Human hermaphrodites are extremely rare.
Pseudohermaphrodites have the internal sex organs of one sex, but the 
external appearance of the other. The true sex of the latter becomes 
apparent at adolescence when the normal hormone activity appropriate to the 
internal organs begins to function. Human pseudohermaphrodites show 
functional disturbance of the endocrine glands, especially of the pituitary 
or adrenal glands, and do not possess two sets of functioning sex organs. 
Because of the homology between male and female sex organs, it may be 
difficult to tell whether a human hermaphrodite is a female with 
overdeveloped  clitoris or a male with underdeveloped penis, cleft scrotum, 
and nondescendant testes. Recently, many persons have undergone surgical or 
hormone treatment to modify their nonfunctioning sex characteristics and 
emphasize the sex indicated by those that are functional.

This answer is a composite from two sources: 
The Hutchinson Family Encyclopedia, Helicon Publishing Ltd 2000
Funk & Wagnalls Encyclopedia as provided on the InfoPedia CD-ROM

Hope that helps
Jurgen Ziesmann