I was wondering two things: have scientists ever studied incorruptable saints? If so, what were the conclusions? Also, is there any Christian basis for ghosts or do any Christians believe in something like ghosts?
Christians believe in souls, though it is remotely possible(i.e. only Jesus can do it) to bring a soul back into a dead body.
Yeah, but do Christians believe that souls, sans body, walk the earth?
Well, my sect (Covenant) sure doesn’t. Unless you consider angels or demons ghosts, I’d be pretty sure that no Christian Church believes in ghosts, though individual Christians might.
The Skeptic’s Dictionary on incorruptible bodies. Brief summary: claims of “supernatural” preservation of corpses usually result form a) good environmental conditions for preservation and b) ignorance of the normal range exhibited by decaying bodies.
As to “incorruptible” saint’s bodies, what I’ve read seems to point to not so much truly incorruptible, but that they don’t just bloat, stink up the place, crawl with maggots and eventually become crumbling bone fragments in the expected manner and time period. IOW, the “incorruptible” saint somehow becomes “mummified” without benefit of any evident embalming or propitious environmental conditions. St. Francis Xavier’s cadaver, for instance: his skin, quite a bit of his hair and much of his (dessicated) flesh are still on, he’s not the pile of bones you’d expect after sitting for 4 centuries in the tropical environment of Goa, India; but he DOES look 450 years past his freshness date. Link to pics at the bottom of this page
As to wandering souls (ghosts), most forms of Christianity AFAIK teach officially either that the souls head on out to Heaven/Hell/Purgatory(if applicable), which are places away and distinct from out physical world, or that they go into "soul sleep"awaiting the Resurrection/Rapture; either way you don’t hang out on Earth taking care of unfinished business. Traditionally, churches treated “ghost hauntings” as demonic possessions and applied exorcism.
Communication with the “other side” is a different issue. The Bible forbids necromancy but in the Old Testament, King Saul defies the ban to summon the spirit of the dead prophet/judge Samuel (who promptly tells Saul he’s toast) – thus implying that it COULD happen, but is just a very bad idea. Then there is in Catholic tradition the visions/apparitions of saints, divinely granted signs where God uses a specific soul to carry a message. None of these is the same thing as lost souls stuck on the earthly plane and getting in the way of the living, or waiting by the phone for John Edward to call.
Since at least 85% of the population of the US calls itself Christian, and about 33% of the population says they belive in ghosts, I think we have to conclude that some Christians believe in ghosts.
…but not everyone who believes in ghosts also believes them to be the spirits of the dead. Many people, including myself, believe that the ghosts people see really are something other than a trick of the imagination, but are more akin to the (energy)residue of an event or a person and might some day be explained by science, rather than believing a ghost to be a sentient spirit trapped on Earth. (Look up " residual ghosts" on google for a better explaination) If you don’t believe that ghosts are spirits it doesn’t conflict with the Christian beliefs about life after death.
I belive in ghosts. I see them on my TV all the time. 
The questions of whether one should believe in ghosts, or what ghosts might be, are ones I leave to personal judgment.
The fact remains, however, that there is Biblical support for belief in ghosts, and so it does not seem to be necessarily inconsistent with Christian belief.
In the Old Testament, King Saul had the Witch of Endor conjure up the ghost of the prophet Samuel. (Just guessing, but that is probably why Samantha’s mother’s name was “Endora” on the TV series Bewitched).
In the Gospels, it says that the Apostles, on first seeing Jesus walk on water thought that he was a ghost. Later, when Jesus first visited them after the resurrection, they thought he was a ghost. Rather than tell them that are no such things as ghosts, Jesus tells them that, unlike a ghost, he is solid flesh and blood.
As for incorruptable bodies, as a previous post states, it appears that generally or always the bodies are not free from decay so much as they are holding up incredibly well. History records that after Francis Xavier died an investigation was ordered. IIRC, about a year after he died a doctor was ordered to conduct an autopsy to determine if it had been embalmed in some way. The story is that his first incision drew fresh-looking blood and the inquest was called off. I have heard it said that Xavier’s body did not begin to wither much until the 20th Century.
James Randi tells a pathetic story about St. Bernadette. Supposedly a few years ago a television company arranged to shoot pictures of her body. Under the hot lights they used, her skin began to warp; it was, in fact, the sort of wax used in wax museums. I’ve since heard that the authority maintaining her body claims that it was really her body they displayed, but that it has been “touched up” because of limited decay which has occurred over time.
There are rarely-used techniques known which can leave an embalmed body in a remarkable state of preservation for many years. It is said that the embalmer flushed out Evita Peron’s circulatory system with glycerine prior to embalming, and this is what caused her extended preservation. After Lenin died the Soviet government issued a statement that a revolutionary new technique had been discovered which was used to preserve his remains. For years while the Soviet Union was an ongoing entity the National Review obsessed over the possibility that the body in Lenin’s tomb was really just a wax dummy. It would appears that this would have been revealed by now if it were true, but I haven’t heard anything about it.
There are also specific burial places where bodies are said to unacountably remain in a state of preservation for centuries. I have heard this claim made several times about a crypt under St. Mickens Church in Dublin, Ireland, where one of the bodies is that of a Viking chieftain.