My daughter is 16, do I need my wife's permission (signature, legal papers) to leave the country for a few weeks? We are not divorced but not really talking.

Are you separated? If so even if you haven't started court process then I would make sure to get her permission. Get the proper paperwork from her so you don't have problems in your travels.

If you are traveling without your wife, then yes you will need her written permission for your daughter to leave the country. Does your daughter have a passport?

Here's a good template for the letter that your wife should sign - and note that you should have this this with you even if you weren't having marital issues:

http://photos.state.gov/libraries/unitedkingdom/164203/cons-acs/sample_letter_of_consent_to_travel.pdf

The form to which ebaines linked appears to be good. The custodian who is to travel with the child might also want to have a certified copy of the child's birth certificate. Otherwise, matching the child's surname to the identity of the child's parent might be difficult. Also, if there is a custody order, a copy of that would be good to have.