Here comes round 2 in catching up with Rodney Smith's Table Talk!
Storing Games is a pretty simple answer. Time to talk back!
There is no one-size-fits-all solution for keeping your games organized. Just like you've got different size boxes, so also exists solutions.
I have a selection of games tastefully arranged on a bookshelf in my living room, for easy access.
These are not all my games, but they do represent the games I see the potential for playing. Multiple drawers, shelves and nooks within my illustrious manor contain games elsewhere…but these here are the condensed "best of" that either me, my wife, my friends or my children have requested. For instance, the kids occasionally like Cootie. It is not a pleasing game to play. By comparison, however, they have never once asked for Hi Ho Cheerio which is also in my collection. In the case of Hi Ho, it sits wrapped in chains at the bottom of a hole. Cootie, on the other hand, receives a honored position next to the Play-Doh.
By forcing myself to stick to this one corner book case, It helps limit my board game acquisition to a reasonable rate as well as concentrate my thoughts on which games my family values the most.
Very few board games have good inserts, and for the most part everything is going to be going into bags. I try to group together counters and playing pieces that will be used together.
Mission: Red Planet is a pretty well organized game. A few pieces float around the board, but most of the components start in the hands of the individual players. In this case, I put a single bag together for each player…this "player bag" contains both the cards and the astronaut tokens each player will need for the game. Ticket to Ride and similar follow the same procedure.
Galaxy Trucker I took a completely different tactic with. With Trucker, everything starts mostly in the middle of the board except for the individual player boards. I put the pile of ship tiles in the big bag. I put all the misc components like the die and the sand timer in the little bag. Then I put all the little tokens and money in a plano (tackle-style) box so people can "fish" (ha-ha!) out exactly what they need as the game progresses. Otherwise, dumping out all these components and then picking them back up again is a huge pain.
I would probably do this with games like Puerto Rico as well. However, I bought Puerto Rico in the dark days before I really thought about game storage. So instead everything is in about a thousand bags, which I am always reminded of when someone actually wants to play it and I open the box up. Prêt-à-Porter is the same way.
A lot of people use sleeves. Other than my Magic Cards, none of my card games have been sleeved. Both Citadels and Race for the Galaxy see a lot of play, and the cards are still looking good enough I don't consider the wear a problem. The sleeves on my Magic cards are mostly there to cover up the wear from the decade or so before sleeves were even in my vocabulary.
I do have one board game I've sleeved the cards in, and that is Dungeon Twister: Prision. And these cards are never shuffled! But they do get picked up and tossed down on the table pretty frequently. And my son, who went through a big Dungeon Twister kick does sometimes (always) have sticky hands. So into the sleeves the cards went!
So not terribly exciting. Getting more into the board game hobby has got me more interested in all the other aspects aside from playing. But usually, when I'm considering the other aspects too heavily its probably time to start thinking about playing instead.
Lately, the most played game in my collection is Tsuro. And the organization of Tsuro involves dumping everything back into the box at the end of the night. Believe it! Both playing pieces and tiles are super heavy-duty for days of playtime even at the hands of toddlers. And the insert keeps everything rattling together in a central channel, surrounded on 5 sides by cardboard and the thick playing board laying across the top to keep anything from jangling out. So some games get it right by design or by luck!