When is variable speed important in an angle grinder?
When shopping for an angle-grinder, how important is variable speed? 

The importance is use dependent. I think that using different disks (grinding, sanding, cutting, brushing, etc.) is a satisfactory way to get the most use from the grinder. I've never had any desire for a grinder that would go a different speed. Actually, I think that controlling the grinder is probably easiest at top speed.

For which uses?

Generally a grinder is used for working with steel, in which case one speed is fine (that's what I have- no complaints). I have also used it for sanding patches of concrete; dust is a little problem, if/when it gets in the motor (maybe it should be wrapped with a rag-filter- but don't let the rag get caught in the wheel, or else). I suppose that if you are an artist or you're using a grinder for high precision, or on delicate or soft material, I could understand wanting the grinder to go more slowly, but then again, maybe not.