"When an unseen force commits several murders wherever a young woman is present, Mulder suspects that it is the spirit of the woman's former boss who was believed to have committed suicide, but was actually murdered, and he is protecting her."
X-Files – S1E5 The Jersey Devil
"The murder of a homeless man, which is very similar in detail to a murder committed in 1947, leads Mulder and Scully to a legendary man-beast roaming in the forest near Atlantic City."
X-Files – S1E4 Conduit
"Mulder and Scully travel to Sioux City to investigate the disappearance of a teenager, Ruby Morris, whose mother Darlene claims was abducted by aliens."
X-Files – S1E3 Squeeze
Scully and Mulder discover a mysterious serial killer when they find that their current investigation is similar to an unsolved case from 1903.
X-Files – S1E2 Deep Throat
"Mulder and Scully investigate the mysterious case of a military test pilot who disappeared after experiencing strange psychotic behaviour."
X-Files – S1E1 The Pilot
The meeting of Agent Mulder and Dr. Scully is one that has gone down in the record books of the 90s and it took place on September 10th, 1993 during the Pilot episode.
The X-Files – The Overview
I hope it's as good as Eerie, Indiana mixed with Are You Afraid of the Dark?.