Take "Coke", for example. In parts of the Southern United States, a coke can be
any kind of sweetened carbonated beverage. A soda or pop (or whatever you say), no matter what the actual brand, is considered a coke.
This is a classic example of a brand name becoming generic. Coca-Cola has even sent representatives to restaurants to make sure that when a customer orders a Coke, he isn't given a Pepsi or some other perceived equivalent. This is a negative consequence from Coca-Cola's perspective, but of course such a consequence only arises as a result of dominant position in the product category. Even if the brand could be considered diluted as a generic name for the product itself, the brand recognition is still strengthened and its staying power is solidified for many years to come.
Another example clear example is Kleenex brand tissues. In our Tissue vs. Kleenex poll, 66% of respondents say Kleenex instead of tissue.
Other brand-name-as-generic examples include the following:
Band-Aid as bandage (at least a small, disposable one)
Scotch tape as invisible tape
Walkman as portable music player (although MP3 players have certainly changed this)
There are many more examples that you wouldn't even suspect were ever brand names, such as "dry ice".
Google has even managed to make its brand a verb. As far as I know, this hasn't happened since Xerox became the verb "to photocopy", as well as the noun for "photocopy".
Can you think of any good examples of genericized brands?