I once saw Michael J. Fox at a charity event, and one of the fans asked him if the reason the DeLorean always broke down whenever it was used was because God disapproved of time travel. The threat of he and his loved ones being erased from existence, was that a warning somewhat similar to others God has sent (for different reasons)?
Before I proceed further with this discussion, I ask two things: first, that we all engage in this discussion with as much respect for each other's religious opinions as possible and secondly, that those that may be offended by a religious discussion choose not to participate and read no further.
In preparation for posting this, I read through the religious text with which I'm most familiar, the Bible, but could not find anything related to time travel. I did some searching on the Internet and while I found some discussion, I could find no actual scripture addressing it. I understand there are many other holy books out there, and I'm hoping that those more familiar with the Qu'ran and others can offer up any references they find.
Once time travel is possible, the first application is likely to be religious in nature. I'd imagine one of the first trips would be to travel back and witness our own origins ("Genesis", in Christianity). The next trip may be to witness our endings ("Judgment Day"). And at some point I would imagine we'd travel back in time to connect with key individuals and prophets. All of these trips would have tremendous religious overtones and we'd be deeply reliant on religion not only to put whatever we learned into context, but to make the right decisions about who to send, and when, and how they should conduct themselves.
Think about it - if tomorrow there was an announcement that we could send a man back or forward through time, who would we send, where would they go, and what would we hope to learn? Those are not scientific questions, and Stephen Hawking couldn't help us.
Let the discussion begin. :)