I normally just delete them and then manually type them into a new adgroup. I dont think there is a way to automatically move them though. Cheers Stewart
Look in adwords help for the "Adwords Editor" - it's a programme you download that lets you do loads of useful things, including moving or copying keywords in bulk.
yeah there's no better way to do it than with editor, I mean for most of us that dont use any API stuff or so. it will not only help you to move keywords from one group to another, but it will also allow you to do so with adtexts, campaigns, and so on. even if you've got several accounts, you can copy/cut data from one account to another. You'll also be able to export your whole account, campaigns or current view, which is handy if you want to get your account back as it used to be after possible mistakes.
dont delete the keywords if you intend to move from one adgroup to another, Instead just pause it., Incase if the keywords sitting in the new adgroup is not working for you, you can always resume the old one.