You don't need a passport to leave this country. You may need one to get back in. I've walked across both borders many times without needing paperwork of any sort. The northern border especially is quite porous.

But it depends on your intentions. If you are planning on commercial travel to a populated area outside the US, you must have papers.

Where are your papers, comrade?
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The ultimate result of shielding men from the effects of folly is to fill the world with fools.
-- Herbert Spencer, English Philosopher (1820-1903)