Tarot bags are a very popular way of safely storing tarot cards. My favourite bags are Sulis's handmade tarot bags. She makes gorgeous velvet and silk lined bags in a number of colours, styles and patterns, and reading cloths as well.
Lo Scarabeo sells quite a few tarot bags (as well as tarot decks and sets) on Amazon.com.
There is also a wide range of tarot bags and pouches on eBay - patterned, decorated, embroidered, velvet and more.
For something sturdier to keep those special tarot decks, there are always tarot boxes.