Bio: William Mulder, a former employee of the State Department is also Fox Mulder's father. A cold, unsmiling man he also seems to have worked on "the project" and been involved with the MJ files. He knows the Cigarette Smoking Man well and they had worked together at the Center For Special Warfare in North Carolina and on a secret assignment. When they learn of the danger of their work being exposed (Anasazi), William Mulder is extremely worried that his son would find out about his involvement in the cover-up.
His relationship with his son generally seems remote and withdrawn - he flinches when his on tries to hug him preferring a handshake instead (Colony). He is as stiff later when a guilt-ridden Mulder breaks the news that Samantha is "lost" again (End Game). This icy reserve is seen in his relationship with his wife as well and their marriage seems strained.
When he finally meets with his son to confess his part in "the project" and it's overall significance, he is shot dead --- seemingly by Alex Krycek on orders from the CSM. His last words are to his son, begging him for forgiveness. His son is framed in his murder but eventually proclaimed innocent of it. After his father's death, Fox finds out that his father had previously too threatened to expose "the project", at which point Samantha Mulder was abducted to ensure he maintained his silence.

Quotes:

"The certainty... becomes a comfort that allows you to move on. We bury our memories so deep after that has been destroyed." (Colony)