Create a new box from your existing vm:
cd into the directory with your Vagrant file
run vagrant package This will export a box file called package.box by default
run vagrant box add foo package.box to add package.box to your existing boxes. (Assuming you are using VirtualBox and not VMWare)
run vagrant box list to verify it was added.
Now you can just create a new folder, run vagrant init as normal and set your box to the following:
config.vm.box = "foo"
The new VM will spin up with the exact data that was present in the previous VM.
Vagrant Documentation
Additionally checkout a new product from the creators of Vagrant called Packer. It will do this same thing, but allow you to copy your vm's to other providers (Amazon, VirtualBox ect..)
Update
Newer versions of Vagrant have two commands that make the above steps unnecessary.
vagrant share
vagrant package
Vagrant share will upload your box to atlas
Vagrant package will create a .box file automatically.
For more information, type in vagrant --help