"What influenced you most?" is the correct form. This is called a subject question (ie. no inversion or auxiliary verbs: the subject just replaces the question-word in the answer). To compare, "What did you eat for lunch?" is an object question. Notice the subject is "you", and what the question asks for is the object of "eat". You need a very specific situation to ask "What did influence you the most?" In general, this form is not correct.

The second question is more commonly used. However if you ask the first question to an English-speaker, they will probably understand you.