Can I export Alexa's keyword data?

Yes, you can export site keywords and keyword opportunity lists.

To export site keywords

1. Go to https://www.alexa.com/pro/keywords/site/
2. Enter a site URL
3. Click the "Export CSV" link at the top of the page

You can also export paid and paid competition keywords.

 

To export keyword opportunity lists

1. Go to http://www.alexa.com/pro/kwopportunities
2. Enter a query
3. Set the filters so that the list returns the keywords you care about most
4. Click the "Export CSV" link under the filter list 

Note that all keyword exports are limited to 1,000 lines.