Does Adwords have a Keyword Suggestion Tool?

Yes, but you need to be an Adwords advertiser to access the tool. 

Once you are logged in, click on the 'Campaign Management" tab, then on on the 'Tools' link, then on 'Keyword Suggestion Tool'. Enter one keyword or phrase per line and suggestions are tailored to the language and country you selected. The results show popular queries that include your keyword and there are separate lists for related queries and any relevant suggestions.