I think when referring to the entire group of years that make up an entire decade (and thus indicating plurality), the proper form is 1920s without the apostrophe because you are essentially stating the following: "all the years that make up the decade which begins with the year 1920" when you use this construction.
When trying to indicate that something belongs to a particular decade, you may use the apostrophe to indicate possession. For example, the apostrophe in the phrase "1920's music" would imply that you are referring to music that was composed, published, recorded, or popular during the decade which begins with the year 1920. In this case, the music belongs to the decade.
As others have said previously, the apostrophe is a way to indicate that something in a word is missing. In one case, it may indicate the omission of numbers (ex. '20 instead of 1920). In another case, it indicates the omission of words which may be used to expression possession (ex. 1920's music instead of "music that was recorded in the decade that began with the year 1920). It is never, never, never used to express plurality.