Investigation with occult/scifi/conspiracy elements? If you're not against pixels, I think many of the adventure games from wadget eye may fit the bill. Especially Gemini rue, Technobabylon and Resonance (they're scify, but if you're willing to include Blade runner, they fit)
their page here I also remember "the moment of silence" felt pretty xfilesish when I played it, but it was a long time ago, so I can't say much about it
Breja: What about the Still Life games? They look like they might fit the bill.
I played the first. Investigation with a very creepy atmosphere and some strange stuff, but not really supernatural. Might fit the most "mundane" parts of x-files.
Another one if you're into gaming archeology : Bureau 13 was pretty much "X-Files' men in black - the game". Old stuff, though (1995), and I remember it was buggy as hell.