Regular film cameras existed, polaroid existed, and I checked and Apple released their Digital Camera in 1995. So even for digital photos it would have been possible, at least for season 3 and on...Here you can see the photo quality is decent http://en.wikipedia.org/wiki/Apple_QuickTake#mediaviewer/File:Quicktake-bild.jpg
So, Why didn't either of them ever bring a camera? I understand that in the case of the main conspiracy arc storyline with visitors, deepthroat, or smoking man they would have caused interference, stolen, or smashed the camera. But episodes like the Aging Ship comes to mind. He could have taken photos of the aged ship, the plaque, himself and Scully.
And I'm not saying that would have made his stories more believable, or substatiated them, but part of the "Investigation" process (in real life) is to document your findings. So why are all of their reports based on hearsay and eye witness accounts?