Not sure about ghosts- we've got proof in the form of orbs that may or may not be dust particles, static voice recordings that may or may not contain voices of the dead, etc. Nothing really solid. But, as the saying goes "absence of evidence is not evidence of absence."
There have also been many UFO sightings. Why hasn't there been any proof of aliens then?
Because ghosts and UFOs are names people give to things that don't exist, but they swear they saw.
Careful there- US Air Force officials recently stated that during the cold war, about 18 nuclear missles, in their silos, were suddenly disarmed, while a glowing light was no further than 30 feet in the air above the main gate, spooking the guards (who were ordered to keep it from entering the base.) Then there's a European country (Belgum or Switzerland, I think) that actually treats UFOs as something more than a mass hallucination. Then you've got unexplaned "radiation" burns, strange scars, EM interference, radar blips for said objects, symptoms of PTSD around certain areas/objects after an apparant "abduction" incident, missing embryos (as in, no embryo but no sign of miscarrage)...
There's more evidence for UFOs than there is for ghosts (well, more evidence that's harder to explain away.) But it's all still circumstantial- they may be aliens or some unknown phenomenon, but it's really unnerving when you're staring at the 5% of reported cases can't be explaned.