A Little About Chess Set Collecting
I haven't seen anything on Chess.com about the collecting of chess pieces and boards but its not uncommon to see chess sets in living rooms that are not made to be played with but are merely decorative.
Of course there are chess sets that can be admired and used. Those represent a unique accomplishment by a craftsman. Aesthetics is an under appreciated part of Chess and Go as well. A chess set must be comfortable to play with, draw you into the game itself and yet not be distracting. A purely decorative set can take liberties because distraction is a non-issue.
There is also the possibility of collecting chess sets as antiques but that is a riskier proposition than many other categories of antiques. Games have been around since recorded history and they have been artistic and elaborate but they did not come with the certifications that fine furniture, etc. have come with. Chess sets are harder to authenticate and determine time period. Obviously that will affect value and it's easy to get burned or even defrauded.
A good place for a collector to start would be interesting chess sets regardless of era or just Do It Yourself like this set http://www.popularmechanics.com/home/how-to-plans/a22075/how-to-make-a-simple-chess-set/ . This article has some further examples of DIY chess sets. Here is a set made from brass by a true artist http://www.popularmechanics.com/about/a18680/chess-set-crafted-from-scratch/ who is just as likely to make a working electric look like an AK-47 rifle.
Or how about these 9 DIY chess sets.
Grandmaster Yuri Averbakh who has written some influential chess books is also an avid collector and a member of the Chess Collectors International. You can read an interview with him about the ancient roots of chess here.
If all this has got you interested in collecting why not check out the Chess Collectors International Beginners Page.