Brands that attain eponymic status are saddled with a blessing and a curse. On the one hand, I can only imaging the elation that went on at Google's headquarters when their company name mutated into a verb, but on the other it foretells of darker times ahead.
The problem is that, given enough time, the totemic nature that comes with such a strong brand image dilutes the entire marketplace - if it looks like a Q-tip and functions as a Q-tip, the fact that it's labeled as "cotton buds" hurts nobody but Unilever. Likewise, a time will come that saying "Just Google It," (with apologies to Nike) will cause people to fire up their search engine of choice and not Google specifically.
There are ways to combat this, but all are stopgaps. Heavy advertising is one way - much like trademark protection policies that essentially amount to a 'use it or lose it' mentality, by keeping the brand at the forefront of the public consciousness it can be assured that thinking of the eponym still relates to the product.
Product innovation is another way - if the brand keeps evolving (like Gillette's Mach 3 line of razors) it gets hard to pin down. This is more a way to avoid eponymic status than to deal with it once that status is attained but it can be useful after the fact, in that thinking of the eponymic brand also makes a person think of the other products offered by the company - it's a way of using the strength of the big name to push a company's lesser known products: razors selling shaving cream, or copier companies branching out into the printer business.
Either way, eponymic status is more of a milestone in a brand's life cycle than an insidious, little-guy destroying conspiracy.