I would like to run Google AdWords campaigns with the keywords as my competitor's brand names. Some questions:
It is a fairly common practice and is especially effective if the competitor does not target ads to their own brand name* (some do) and your ad is the only one that will show up.
Targeting to the brand name is legal, as long as you don't use the brand name keyword in your ad, which will reduce its relevancy and cost a bit more than your typical ad where keyword matches a phrase in the ad itself. Using any part of the competitor name in your ad becomes an issue of a trademark infringement. The next best thing to brand name is the description of the product - if your ad is messaging about similarity in product and perhaps value (or better), thank you might be able to steal some of your competitor leads.
I personally think it's not a bad way for a new company in an established space to drive traffic to their site, as long as ROI works out, e.g. the sale price and conversion rates are high enough to justify the cost of advertising.
* In case you wonder why would a company target ads to their own brand name instead of using free traffic - if the brand is very established and search results pull up too many of its pages and they want to take users to a specific offer landing page, it makes sense to do it. Big brand example - New York Times subscriptions.