In psychological terms, a man's anima is the inner feminine aspect of his own psyche. Complexes that can affect the development of his anima begin with the first female figure he encounters, the symbol of the mother.
In our myth (X-files, for those who need reminding) we see our hero's (Mulder's) anima personified in a number of ways throughout his journey, the primary incarnation being that of Scully.
But before we explore the details of that particular relationship, we must examine the incarnations of the anima in our hero's early development. First, of course, there is his mother. This character is presented to us as caring, if slightly detached. From what we eventually learn of his early childhood, this was a comparatively normal relationship with a fairly common level of dysfunction.
However, his anima development is abruptly arrested in its normal development at the age of 12, with the defining event of his adolescence and early adulthood, the abduction of his sister Samantha. This causes a monumental shift in his relations to the mother; and here we can observe an almost Freudian split in the mother symbol, wherein his actual mother and his relationship to her become the foundation of the personality of the darker side of his anima. Consequently, the figure of the sister, who though her primary function in this myth is that of the divine child, at his point also takes on an anima/mother role as the hero projects onto her the characteristics of the "good mother" and thereby sculpts his anima's positive characteristics around this immature and idealized figure of loss and sacrifice.
As our hero moves through his adolescence and into early adulthood we see his outward personality and relationships greatly affected by this catalyst event and its symbolic ramifications. We observe almost textbook manifestations of his anima complex, in that we now see a man who is emotionally and intuitively driven, sometimes to the exclusion of logic, and who devalues women, both in his choice of his quest over his romantic attachments (the primary examples we're given being Phoebe Green in the episode "Fire" and Diana Fowley whose relationship with Mulder is alluded to in seasons 5-7), and in his habitual use of pornography and adult entertainment (something alluded to periodically throughout the earlier years of the series).
His early romantic relationships further reinforce the origin of his issues, in that we see him being drawn to women with dominant, and at times hypersexual personalities. These relationships, as we have noted, cannot survive in the shadow of his idealized relationship with the figure of his sister/mother/good anima (Samantha), inevitably dooming him to repeat the traumatic break down of the relationship with his mother when he finds himself continuing to re experience the betrayal and emotional abandonment caused by his mother's actions and responses at the time of and since his sister's abduction.
We should also note here, that his idealized relationship with his positive anima, up to this point embodied by his missing sister, is the cause of a great deal of guilt in our hero. He failed to save his sister on the night of her abduction and has since failed to be able to find her, and as a result he adds to this guilt every time that experience causes him to fail in his adult relationships with women and adds fuel to his tendency to fixate on cases of missing persons in his work as an investigator. This sense of guilt and unfulfilled obligation becomes a major obstacle as his relationship with his anima moves forward in its evolution.
So this brings us to the point at which we meet our hero. We find a man with an extensive anima complex, that has affected his personal and professional decisions. All of his anima interactions have amounted to, what we in the modern vernacular would call a "virgin/whore complex", in which there is one ideal of woman held pure and sacred, while all other women reflect the earliest stage of anima development, that which Jung called "Eve", in which the female is the object of desire, yet simultaneously viewed as evil and ultimately powerless.
At this point I will diverge briefly and touch on the symbol of the shadow as it has manifested itself in our myth. I'll insert a definition here for those who might need further clarification as to what the "shadow" is.
Wiki":In Jungian psychology, the shadow or "shadow aspect" is a part of the unconscious mind consisting of repressed weaknesses, shortcomings, and instincts."Everyone carries a shadow," Jung wrote, "and the less it is embodied in the individual's conscious life, the blacker and denser it is."  It may be (in part) one's link to more primitive animal instincts, which are superseded during early childhood by the conscious mind. According to Jung, the shadow is instinctive and irrational, but is not necessarily evil even when it might appear to be so.
As a consequence, the shadow is prone to project: turning a personal inferiority into a perceived moral deficiency in someone else. Jung writes that if these projections are unrecognized "The projection-making factor (the Shadow archetype) then has a free hand and can realize its object--if it has one--or bring about some other situation characteristic of its power."  These projections insulate and cripple individuals by forming an ever thicker fog of illusion between the ego and the real world.Jung also believed that "in spite of its function as a reservoir for human darkness—or perhaps because of this—the shadow is the seat of creativity.
In the case of our hero and his development, up to the point at which we first encounter him, the shadow is very well developed and is represented primarily by the "syndicate" or the "shadow government", specifically the figure of the Cigarette Smoking Man. There are other manifestations of the shadow that we will explore at another time, but those mentioned here are the ones that have bearing on the subject at hand.
Our hero up to this point has, as we have just discussed, projected his positive anima into the figure of his missing sister. But as the shadow can at times work mysteriously to our benefit, we see that at this point it introduces a new female (Scully) into our hero's world. The shadow's stated intention in bringing her into the equation is nefarious. She is instructed to discredit and debunk the hero's work, or in symbolic terms, his quest.
This figure, however, seems to have a will all her own, that we can see have a positive impact on our hero. She is, interestingly, the polar opposite personality of the anima complexed figure of our hero. She is rational, logical and scientific, a rigid contrast to the fluid and kinetic disposition of Mulder.
Upon meeting this new figure, our hero's initial response is to immediately project his negative anima's image onto her, knowing as he does, that she has come from the shadow, and is therefore a perceived threat. His interactions with this new anima figure, however, contradict this preconceived notion of her motives and allow him to form a new level of respect for a woman, and thus, he takes a step forward in his development when he takes her into his confidence and places professional trust in her. His overall anima now moves into the stage of "Helen", for which I will again I will defer to the Wiki definition for simplicity's sake.
"The second is Helen, in allusion to Helen of Troy in Greek mythology. In this phase, women are viewed as capable of worldly success and of being self-reliant, intelligent and insightful, even if not altogether virtuous. This second phase is meant to show a strong schism in external talents (cultivated business and conventional skills) with lacking internal qualities ( lacking faith or imagination)."
So thus far, we have established the dynamic that characterizes our hero's interaction with this new anima figure in the early portion of this myth. The next major event in this evolution comes when we see Scully abducted herself ("Duane Barry" through "One Breath") . Here we see that she is beginning to acquire some of the symbolic significance that was previously concentrated in the figure of his sister. The extent of this transference is later demonstrated more concretely, when Mulder chooses to save Scully over the woman who he believes to be his sister (End Game).
It is at this point in the overall story, that we see the hero's first major rebirth, (Season 2-3 cliffhanger series) and simultaneously, we see the anima begin a gradual progression into the third stage of development, which Jung named "Mary".
Wiki:The third phase is Mary, named for the Christian theological understanding of the Virgin Mary (Jesus' mother). At this level, females can now seem to possess virtue by the perceiving male (even if in an esoteric and dogmatic way), in so much as certain activities deemed consciously unvirtuous cannot be applied to her.
In this phase of our myth we learn more and more of the spiritual side of Scully, as demonstrated by her seemingly psychically based faith in Mulder's return in "The Blessing Way", and her relationship to religion and Catholicism.
I'm going to stop abruptly here and continue this in another post if that's not too confusing...this is just getting to be quite long and this new phase seems like a good point to press pause.