AdWords does not provide information on what keywords your competitors are bidding on. However, there are a number of tools outside of Google that can help you analyze who's ranking on specific terms, as well as what keywords individual domains are showing up for.
Several competitor keyword tools provide free basic searches but do require monthly subscriptions to access the full data. You'll need to sign up for the free trial, if available, or purchase a subscription to download all of the keyword data.
The following are some competitor keyword tool options you may wish to consider: