I've been in mgmt for most of my career, and hired many, many people and also had to deal with resignations and occasionally let people go (hardest part of the job). What I can tell you is that your work record, whether on your resume or not, is most important to any new prospective employer. And gaps do not look good.
So, for sure take the high road. Give them 2 weeks notice or longer (if you are a long time employee). If your employer feels that you are a risk (competitive or other reasons) or negative influence on peer workers, then they may ask you to leave early and pay you the remainder. But no notice will not encourage a good word, if your past employer is called up (even though you don't list them as a reference).
It is not necessary (and often undesirable) to give a reason in your resignation letter. But if possible, you should go on good terms, and reasons like "moving" or "going back to school" or even "switching careers" can ease tensions. A smart employer will want to do an exit interview (by someone other than your immediate supervisor or manager though), and that is your opportunity to give feedback, but still always taking the high road.
Good luck.
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