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The title says it all for this one. Keep your surveys simple and don't over-complicate them. You will get more results and you will have more data to work with. In short - keep it simple.
What makes a simple survey? What makes a survey over-complicated? Out of the two I think it is easier to ask what over-complicates the survey.
Any sort of unneeded gates, such as logins or registrations, overcomplicates your survey. These create an immediate barrier for your users and they end up leaving your survey.
Lengthy questions with bad grammar or spelling, overcomplicates your survey. Get right to the point in your questions. if you provide an essay users will not read it and just choose a random answer.
Too many questions, over-complicates your survey and will kill your audiences interest. The first few questions might get answered but you will see drop off as the survey progresses.
Asking unrelated questions, over-complicates your survey. If you ask questions that are not relevant to your target audience then you will either get bad data or not enough responses. Make sure that your questions are targeted to the right people.
Questions that offend, are rude or otherwise insult, have no place within your survey. There is no reason to go into depth - these should simply not be included.