I can pick a few verses from here to show some Biblical backing on the stigmata:
Galatians 6:17 ESV
From now on let no one cause me trouble, for I bear on my body the marks of Jesus.
1 Peter 4:13 ESV
But rejoice insofar as you share Christ's sufferings, that you may also rejoice and be glad when his glory is revealed.
From http://en.wikipedia.org/wiki/Stigmata you can read more on the origin, but St. Francis of Assisi was the first recorded example of someone have a stigmata, but, as is mentioned, Padre Pio (I believe he is now a saint) endured this for 50 years and it could be investigated by modern doctors.
The fact that there are some examples of non-Christian stigmata was interesting, but when someone is close to God and they are blessed with the stigmata, and it brings them closer, it appears to be from God. But, as when someone does miracle healings, we have no idea if these are truly from God, we have to take it on faith, and look at the fruits from that tree (does that person bring Glory to God for example).