Not all traditions are worth keeping or worth submitting to; in particular, employees giving employers two weeks' notice of their impending departure from said company is one of those courtesies which should, at times, be violated. Every State of the union is a State that has a law that private enterprise employees are employed at will, which basically means that your employer can fire or replace you at any time without notice to you, although there are some States that stipulate certain specific exceptions to this general rule. However, as a rule of thumb, that means, that every day, could in fact be your last day working at your place of employment. Most employees wrongly fail to recognize that this is the reality of how untenable their position and their livelihood really are.
Another error that virtually all employees fail to recognize is that while their personal effects are still their property, by virtue of having their property at their place of employment, means that should they be discharged unexpectedly, that the company will control the access and the timely distribution of any personal property so left behind. That is to say, once terminated, you as a former employee have no legal right to enter back into the premises to retrieve your personal property, it will be returned to you, but your former company will essentially control that process and that timing, and as long as they take care of this within a reasonable framework of time, that is just the way it is going to be. In regards to personal documents that are stored on the company equipment, your chances of getting any of those documents back are solely based at the discretion of the company, since the contents of the equipment are company property, and not yours.
While there is something to be said about providing whatever amount of notice and courtesy that is standard within your company for employees that are voluntary leaving, and as it doesn't behoove most people to burn bridges, there are still significant reasons why you may not want to give a two weeks' notice. For instance, if your standing within the company is somewhat shaky, you may find that upon offering your notice of two weeks, that the company's response is for your immediate dismissal, so unless your new job is capable of accepting you as a new hire, sooner than expected, you will be losing two weeks' worth of salary, something that clearly was never your intention. Another good reason, not to extend your stay unnecessarily, is if your new employment is paying you more money, perhaps even substantially more money, it doesn't make a whole lot of logical sense to work for less money for two more weeks at a company that you have already determined to depart from.
There are, however, circumstances, to which your hand may be forced in providing that traditional two weeks' notice, such as companies that make it a policy within their handbook that those not providing such notice, will forfeit vacation pay or similar, in those types of circumstances, you are better off following your company's guidelines.
While individual circumstances clearly do not allow a one-size fits all policy in regards to providing notice of quitting to your current company, it is pretty much foolishness to stay longer at a company, than is absolutely necessary. The most important thing to remember is that in absence of an agreement that stipulates that you are not employed at will, you really don't owe any sort of notice in return, for if it is good enough for the goose so it is for the gander.