So, by your definition, you want not just a Ghost, but an Apparition: a Ghost with visible, recognizable humanlike presence.
The XBox story was my first thought, too.
This could indeed be a virtual one, a recording of them as in the XBox story, or even an AI, a learning system that has acquired their skills and behaviors at least in the very specific domain in which it is designed to learn.
In the XBox case, rather than merely driving like they drove on their last lap, a learning system could drive like the drove on average, displaying random of their driving quirks; or could drive as they did at their best on each stage of the race, thus driving better in sum than they ever did in life.
A recorded video of someone, projected, would also work. If holograms are possible, then you have the Star Wars "Help me, Obi Wan Kenobe, you are my only hope!" - a ghost of a living person perhaps. Otherwise, you can project onto a wall, or more mysteriously, a stream of smoke, mist, cloud, or water. Could also be a computer-generated sprite texture-mapped with the person's face. Particularly with a low-fidelity projection onto a vague mist, the computer-generatedness would not be so apparent.
But there are other ways to record a person's passing. Perhaps, as they walked from a clearing, they swiped at the thick leaves, and in doing so, either deliberately or accidentally hacked out a person-shaped hole, which, when the sun sets in the evening and shines through it, illuminates the spray from the waterfall. Doesn't even have to be a hole anyone's hacked out - but more likely if done as a deliberate thing. Since the sun moves slowly, you could have it so that only when the light from the sun lit a crystal at a certain angle, it refracted to become a projector - that way you could limit it only to a few minutes, or even a few seconds.
One effect I've seen that caused much consternation was headlights over a hill, which, because of the angle of the road, would shine in the back of a ruined house: the house would look lived in, for a moment, and then would fall dark again as the car moved on. Headlights on hilltops have also caused any number of UFO sightings. So, they make good brief-unexplained-lightings. If a picture is briefly lit by headlights passing outside, and the figure in it appears to because the shadows cast on the picture move, that could be a convincing "ghost" effect. Lightning could have a similar effect.
Another good effect is a moon-halo. Here's a good trick. When the moon is close to full and dew lies upon the grass, look at your shadow: you will be surrounded by a halo. Tell your friend "Wow, there's a halo around your shadow!" (as if you see the halo around his shadow, and not your own) and the odds of him thinking there's something mystical about himself are quite high. When you stand above a mist-covered valley, and your shadow is cast onto the mists below, that has the same effect, writ large. So in this way, someone could be convinced into thinking they see, perhaps, their own ghost, or at least an outline, with a glow from their spirit?
Double-exposure is possible, too: taking shots with a film exposed some years ago that you did not know had already been used to shoot someone else, would show them as ghosts in the shots. Similarly for a videotape with an erase/record head that did not fully wipe the previous data, perhaps.
For more modern digital tech, it would take some kind of software bug - or a virus/malware/joke app that would impose another character into existing video.
In realtime, augmented reality apps like google goggles or yelp's equivalent, let you point your phone at things and see signs for places nearby, etc... what is there was software on your phone that meant, when you pointed your phone camera at something, you say your dead friend superimposed in the shot, or perhaps just their face overlaid over nearby faces that the camera software identified?