Like Christianity it depends on your belief.
Try this website
http://en.wikipedia.org/wiki/True_Cross#Conservation_of_the_relics
Then again, without modern preservation, it is extremely unlikely any kind of wood from 2000 years ago can still exist.
There are numerous churches and holy places that claim to have fragments of the original cross. A quick search will reveal many possible sites. If you go to the Holy Land, you'll find the relic of the Holy Cross being peddled in the streets. Gee, Jesus cross must be bigger than Noah's Ark...
Jesus Christ was crucified on a wooden cross or crucfix if you want to call it that. And yes He died there.
Jesus was crucified in the Holy City of Jerusalem
Jesus was crucified on a wooden cross, not a tree. The cross was used as a method of execution by the Roman authorities at that time.
Jesus was crucified in the nineteenth chapter of John. In Luke, he was crucified in the 23rd chapter. In John, he was crucified in the 27th chapter.
The Roman empire was in power when Jesus was crucified.
There were two criminals crucified with Jesus.
Pontus Pilate sentenced Jesus to be crucified.
No. Jesus was crucified to clean the souls of all mankind if you accept that he died for you.
No, Jesus was crucified during the reign of Tiberius Caesar, who was the Roman emperor during 14-37 AD.
Jesus' followers did not want him to be crucified. Jesus, himself, did not entirely want to be crucified, but he saw the necessity of it and allowed himself to endure the pain for the greater good.
Saint Andrew, one of the Twelve Apostles, was crucified in Patras, Greece, on an X-shaped cross as he did not consider himself worthy to be crucified on the same type of cross as Jesus. Andrew preached Christianity until his death, and his martyrdom is celebrated in many Christian traditions.