Retrieve old addresses with coins that were given away for free to friends and family? Looking for a solution where if I wanted to give away bitcoins or other coins to friends and family for free and being able to retrieve them back if they don't claim it or move it. 

Many times I gave away a few cents worth of btc a few years ago to friends and family, now those cents are worth a few dollars. Some of them didn't take it seriously and just lost the keys that I made for them on paper wallets. 

Has there been a solution to solve this reoccurring problem when introducing newbies to bitcoin?
Just save a copy of the private key.  Then you can import it into your favorite wallet client to retrieve the coins (and sweep them to a new address, so that the key on the paper will no longer work).

When you give the paper slip to the recipient, you should tell them to import it into a wallet and sweep to a new address, so that they don't have to trust you not to steal the coins back.  (Also, this way their coins are secure even if your copy of the key is later hacked or stolen.)  But if they don't do it, you have the ability to take the coins back.

If you didn't save a copy of the private key, and all other copies have been lost, then it is not possible to retrieve the coins.