You may actually have your best luck at local antique shops. Generally, enclosed shelving with doors at those tends to be less expensive than "similar" units at Ikea or other furniture shops.

Additionally, I think you're much more likely to find something with more suitable shelving there -- larger shelves, specifically.

If that doesn't pan out, then you may be in a custom-build world.

Hm. What about large wooden boxes. You can even order them custom made for a relatively cheap price, as they are not very complicated to build.

The advantages are pretty obvious:

1. easily extendable
2. easily to reorder
3. you can partly move them to the cellar or another room if you like
4. take a nice wood and it will look good.
5. you can use them for other things if you ever get tired of them.

Just some examples:

one two three

I think you see, there are a lot of possibilities for every taste.

I keep alot of old stuff (including board games) in really large rattan baskets which are shaped like drums or crates. Rattan is very strong and light. Rattan can be shaped into drums, which makes it easier to roll around when i need to move stuff around.

While the best long term storage solution would be shelves, using big plastic storage containers with lids is a good temporary storage solution. It COULD be a long term storage solution if you don't need to access these games that often or you just don't need to be able to SEE them or get to individual games that often.

The added bonus to using these big storage containers with lids is that you can use them to transport large quantities of games to gaming events. It also protects the games very well. They STACK very well since they have lids. You can move/transport a great deal of games easily with these storage containers.

Have you been looking shelf-style wardrobes at all? Something like this might do.

http://www.amazon.com/Mocha-Double-Wardrobe-Cabinet-Finish/dp/B002FQSC3Y