When Jack first met the Doctor, he was a con man who didn't care for anyone but himself. After him and the Doctor parted ways, Jack wasn't close with many people. He care most for the Doctor, Rose Tyler (and her family), and his teammates in Torchwood (though he acted cold towards them).
He tended to flirt with anyone he met (though it mostly didn't go anywhere).
Though he cared for his teammates, he acted cold towards them.
After he became unable to die, he didn't care very much when other people died (except for the ones he cared for). He himself wished he could die. He was also much more willing to kill (something the Doctor was upset about when they met again)
After being brought back to life by the Bad Wolf entity, Jack is unable to die. He also has a rapid healing rate.
Even though he can't die, he feels pain, and can become wounded for a time.
Even though he is immortal, he has come close to death many times. He was once believed dead for 3 days, and recovered.
WARNING: The canon order of Jack / the Face of Boe is somewhat combined, interfering with the order.
Doctor Who series 1 (season 27):
Doctor Who series 2 (season 28):
Torchwood season 1:
Doctor Who series 3 (season 29)
Torchwood season 2: