Say, someone snaps a picture of me. Do I own the rights to it? Or is it the photographer?
My intent is to find out for U.S. but a plethora of in-depth answers is very helpful!
This varies widely based on jurisdiction, and there are widespread misconceptions about it. The photographer is normally the sole owner of the copyright in the photograph. However, local personality rights (aka right of publicity) may limit the use of an image without permission of the subject. Personality rights vary from nation to nation and even within a nation; sometimes all publication is limited, sometimes all commercial use is limited, sometimes any marketing or promotional use, sometimes only the false implication of an endorsement is limited (as in Canada or Australia), and some places recognize no such right at all (e.g. all US states not listed in the Wikipedia article, such as Oregon). Whether the picture was taken in a place with a reasonable expectation of privacy also may or may not figure into local law.
Country specific consent requirements on Wikimedia Commons summarizes consent requirements for public photos in a limited set of nations. Here's a rough summary of that page:
Some countries where it is illegal to publish (even just on your Facebook page) a picture of a person taken in a public place without permission: Brazil, Czech Republic, France, Germany, Spain, Switzerland
Some countries where noncommercial publication without permission is permitted: Austria, China, India, Netherlands, United States
Some jurisdictions where commercial use without permission is permitted: Netherlands, most US states
In short, as a photographer, you either need to be thorough about acquiring permission, be very careful to research applicable law in your jurisdiction and not exceed the permitted uses, or just take a chance that the person will not have the means and interest to sue you.
One exception: if the photographer is working under a contract that explicitly transfers copyright to the subject, or is being paid by the subject and the work qualifies as a "work for hire," then that party assumes copyright and has full control over its use, and the photographer must license it from them even to use it in their portfolio. (Note that not all work done for money qualifies as work for hire.) If you are a subject hiring someone to photograph you and concerned about misuse, you should consider an explicit contractual clause that limits use without your permission.
Edit now that the OP has added their jurisdiction: personality rights in Washington state, USA are governed by WA ST 63.60.040. If the person's likeness is used without permission to imply an endorsement of a good or service, whether or not for profit, it may be an infringement. There are fair use exceptions. Personality rights are licensable and transferable, and persist even after death for a period of 10 or 75 years, depending on whether the person is an "individual" or a "personality." See the statute for more.
Under Canadian Law, not sure about other jurisdictions, a photo can be published as long as; 1) consent is given or 2) it was taken in a public place or a place with no expectation of privacy. For example... at the beach no problem to take it and publish it, (no expectation of privacy). Through a privacy fence in another persons back yard... not allowed, (an expectation of privacy exists).