Although there is no way to be certain, the plant most commonly believed to have been used in making the crown of thorns is the Euphorbia milii. The Bible does not explicitly mention which plant was used, but legend says that this was the one.
The Euphorbia milii is more commonly known as the Crown of Thorns precisely because of its legendary role in the Crucifixion. It is originally from Madagascar, but it was transplanted to the Middle East before the time of Christ. This thorny plant is also supple enough that it could be shaped into a crown, so it's plausible that the legend is true. What is thought to be a part of the actual crown of thorns can be seen in the British Museum in London, as of 2011.