Recently I read an interesting article from GetResponse about Survey Responses.
From the results looks like it's best to have radio boxes based questions, followed by check boxes. Of course, you do limit useful extra information that the user could be bringing on with open questions – after all, they can only choose answers you picked.
Nevertheless, it looks like keeping to mostly limited questions (radio and check boxes), at most 10 questions, with a few optional open questions in the end is the best way to get survey completions.