Action figure site One Per Case points out that many people store action figures in zip lock bags because they are so convenient and hold accessories, etc. The problem, however, is that most zip lock bags you can buy in stores are made out of plastic that over time is going to expose toys and other stored items to acidic compounds.
The solution is to use non-acidic bags. GZ Zip sells Ultra Clear 2 Mil Bags that,
. . . [are] made from polypropylene [and] are safe for archiving and conservation. Polypropylene is the most widely accepted commercial archival storage material in the United States. It is recommended by both the International Organization for Standardization ISO 10214:1991(E) Sect 4.3 and the American National Standards Institute ANSI IT9.2-1991 Sec 3.3. The polypropylene used in our Ultra Clear Bags is naturally acid free and lignin free and conform to PAT ISO standard 18916.
The cost isn’t too expensive either. One thousand 4″ x 6″ bags are just $20.99 plus shipping.