When you're doubtful about something, you're not sure about it. You might feel doubtful about the picnic you've planned if the forecast calls for torrential rain.
Whether you're uncertain, undecided, or suspicious, you can describe yourself as doubtful. You'll be doubtful about your taxi driver's sense of direction when you pass the same building for the third time. You might also be doubtful about whether or not to try skydiving. Doubtful means "full of doubt," and doubt is from the Old French doter, "doubt or be afraid," with a Latin root, dubitare, "to question, hesitate, or waver in opinion."