Who gets to claim the children on tax returns if we are seperated?

Absent a court order, either of you could claim the child/children and then if there is conflict, the I.R.S. would have to sort out the proper person who would be entitled to claim the exemption/child tax credit, etc.  This conflict usually only arises after the second person files their return.  This could delay any refund to the second person filing taxes, or both of you depending on how you get your refund.  It is correctly noted in other replies herein that whoever provides more than 50% of the support would be entitled to claim the children, however, there is no method to keep YOU or another spouse from claiming a child(ren) initially on a return.   Sometimes it is a matter of who filed first and can get their refund in the quickest manner before the other files and a conflict develops at that point.  Of course, if you file for separation or divorce, the court will award the exemption as part of the final dispostion of all issues and at that point there will be no issues about who is entitled to claim the child(ren).

If you file a separate return, and there's no court order or agreement, the parent who provides more than 50% of the children's support is the one who can claim them as dependents.  The over-50% standard is pretty basic to this aspect of income tax law, whatever the situation.

It might make sense to file a joint return, if you can come to a fair agreement about who gets the refund, or how much of it.  Two reasonable people can treat this in a businesslike manner, and both come out ahead;  if you can do that with him, put it in writing.  This doesn't have to be done face-to-face, and it's the kind of situation that's a natural for a lawyer.