Do Electronic Engineers need to be "licensed"
In the US, it boils down to this : If you can kill people or damage property then you need a professional license. Commercial wiring, you need a license. Aerospace, you probably need a license. But what it really means is you can stamp your designs and certify that the design meets any standards or laws in the field you are working in. You also are required to work under an engineer with a PE for a given amount of time and you must past a test which includes the design process to certify you know how to design things safely.  You then get certified with the state you are working in (similar to other professional certifications like CPA)

If you want to know which subset of jobs for electrical engineering, then look at job postings, it's all dependent on the industry. 

Having a stamp also means you better know what your doing, if the design fails you could be legally responsible for the failure.