The answer to this question is relatively simple - you do, unless you have specifically given that right to somebody else.
Why would you hand over the copyright to your image? Either:
- You are employed as a photographer for an organisation, and you signed a contract stating that any work you produce during work hours is theirs (I have seen some contracts also stating that work produced out of work hours will also belong to the organisation).
- You signed a contract as a freelance photographer handing the rights over to whoever commissioned you. This is common practice in niche areas, such as TV stills, where you may be requested to shoot episodes for a new TV series or film. The commissioning organisation will almost certainly request the copyright to the images, preventing you from posting them to social media and therefore spoiling the plot.
Should you hand over copyright? If you are employed as a photographer, and you want to remain employed, you have no choice. If you are freelance, then you have to consider whether you want to be hired for shoots where you hand over the copyright. I have done this quite a few times while shooting stills for the BBC in years gone by. They pay a premium for the still images, and you are free to use the photography as part of your portfolio. The premium they pay is because you will not be able to sell the images at a later date through stock libraries, for example. As a working photographer, this has always been worth it for me, due to the volume of work involved in shooting TV work.
Why would you want to keep the copyright? So that you have the freedom to do whatever you wish with the photos. You can sell them again and continue to make your living from photography - there is value for a client in using specific images that perfectly illustrate their marketing campaign. Which brings me to the final point, virtually all stock libraries you may work with, won't ask for your copyright - you will simply need to sign a contract, as they need permission to license the copyright to your images, on your behalf.