Can Veneers Be Taken off if I Want Them Removed?

Porcelain veneers are removable , but the need to do so does not arise often.  Veneers are bonded to your enamel, therefore they will have to be removed with a hand piece.  If they are removed they would have to be replaced with new ones.  Make sure that you are happy with your veneers before they are bonded in so that you to not have the need to replace them for many, many years. 

Plastic Veneers are generally used as a mock up to "try on" a new smile beore a more long lasting solution is done. While these are usually reversible, they are not done with any plan for long term use.
Porcelain veneers are made by removing tooth structure and replacing it with porcelain, or not prepping at all and bonding porcelain on top. The bond is so strong that in order to remove the porcelain, it must be ground off with a dental high speed instrument. The removal will permanently scar the teeth, so ALL methods of Porcelain Veneering should be considered irreversible.
This is why it is important to seek care from an experienced dentist that knows how to plan and treat. When cases are done right, when the final restorations are placed, all issues are already worked out.

A traditional dental veneer can be removed and replaced with another dental veneer, but a true return to the original dentition is not able to be achieved.
A feldspathic or "ultra-thin" porcelain can be placed over the existing tooth and can be removed.  That being said, a return to the "previous smile" most likely cannot be accomplished in total as there are adhesives and cements that need to be removed along with the veneers.  Choosing an ultra-thin veneer such as Lumineers, just because "you might want to have them taken off", is a poor reason to factor into such a big decision.   
Find a reputable cosmetic dentist, create a proper treatment plan, work out the details together, and enjoy your new smile.  The veneers should look "right" and you should be happy with your final result.

If you were deem a great candidate for Lumineers ("no prep"), then yes, you can choose to have the Lumineers removed and return to your old self.  If you chose and end up with traditional veneer where the dentist ground and shaved your natural teeth away to place the traditional veneers, then no, your old teeth shape is no longer there.  Lumineers can be reversible where traditional veneers are not.

Typically if you get veneers, your dentist will reshape your teeth.  In that case, if you need to change veneers, you can't go back to your old smile.  Incase you are a candidate for a no prep veneers, then it is easier to go back to your old teeth.  However, do your research, find a great cosmetic dentist that can show you thier before and after pics and enjoy your new smile.