And if you need an online tool while away from your computer, http://getvideo.at/ is running on youtube-dl. It will parse the given webpage and list out direct download links.
Is there a service yet which lets you enter your vine username and receive a zip of your videos? (edit: looks like twitter is planning on building one)
I don't know if there is a service out there yet, but here is a script in python to download all your posted vines and liked vines. You just need to download some dependencies and replace the placeholders with your email and password.