On my 2008 535xi, my washer stopped spraying, but I did hear the pump making noise. I removed the front right wheel and wheel well cover to access the washer reservoir and pump (stupid design, BTW). What I found was that there are little mesh filters that are attached to the top of the pump, and the reservoir was filled with a gooey algae, which had blocked those filters. I flushed out the reservoir, removed an cleaned the pumps and filters, and all is now well..
Last time I was at the dealer, my service advisor confirmed that they are seeing this situation quite a bit, likely doe to BMW's new low-VOC, plant-based, green washer fluid, which does not inhibit microbial growth like the old stuff did.