Yes, you can bid on those terms. But, Nike or Reebok may take legal action if you do not have positive information about their products or you sell their products.
You have been warned. Overture and Google may not accept any responsibility for the advert content and you will be left on your own, if they decide to take legal action.
Large corporations will not write to you to warn you, they have their own legal departments and the first thing will be a legal letter.
There is no reason why they would do this if you sell their products. I have seen some companies bidding on trademarked terms and then they do not sell that brand name's products, but a compatible part to it. They are risking legal action.
Some companies don't like websites mentioning their trademarks and hunt them down to extinction. If you search for some trademark on google and overture and see many different websites bidding on the keyword and using it in meta tegs and page content, this is a good indication that the trademark may be relatively "safe".
I had some issues with a trademark when it's owners lost their top positions in some search engines ;)
To protect yourself, you may want to email the trademark owners that you've got a website (URL here) promoting and selling their products and you are advertising the site using their trademarks and ask them to come back to you if they have any problem with that. A lawyer told me that a copy of this email may help later in case of leagal tensions.
Quickest way to resolve this is to email the advertiser(s) and ask them to remove the listings because they violate your trademark. No need to get agressive, just a polite email explaining the situation. Most companies will respond to this.
If they don't respond within a few days, then contact Overture and they will remove the offending ads.
Google is a little trickier. You have to complete a long form including details about your trademark (www.google.com/tm_complaint.html) and they will investigate - hence it's easier to go direct to the offending advertiser in the first place.