Best method(s) to backup VMs running on HyperV?

Regular file-level backup of only data should still be used - regardless of if the machine is virtual or not. Backing up the disk file however is a great aid in increasing recovery speed for disasters if the entire guest fails.

There are several approaches to backing up the guests with scripting. You could shut it down, copy the vhd and start it again. A clean system backup. But what you probably want though is creating a snapshot. There's also a mount tool to get to the shadow copies programatically so you could actually move them off the volume as well. There's some debate on how stable the VSS-based snapshot system really is and people have lost data. It's a bit (ok, much more) involved than the approach used by Vmware as far as I can tell and is a bit more annoying to deal with.

I think there's a service pack or patch to the Windows Server 2008 Backup tool that makes it capable of backing up the guests transparently by the way?

Also see Microsofts planning for Backup with Hyper-V.

We use System Center Data Protection Manager (DPM) for backing up our Hyper-V machines. It's not exactly a 'cheap' solution but we've found it to be excellent.

You can configure it to automatically take snapshots at varying intervals of your virtual machines. Restoring a virtual machine from a previous time is also a breeze. We have a SAN for DPM's primary storage, but in addition, we also have a decent tape library (which DPM integrates with very nicely) which stores older generations of our VMs.

Additionally, DPM has specific support for SQL/Exchange backups. Certainly works a treat if you have the resources.

I have yet to configure this myself, however...

If you are using a iSCSI (or other SAN) device then that device can often have a feature to backup live images.

If you don't have this option you can use the Hyper-V VSS Writer in Windows 2008 server backup on the host. See here. Or you can use any backup app that supports VSS writers.

The easiest (and cheapest) method is to just use Windows Server Backup in Server 2008.

How to back up Hyper-V with Windows Server Backup

Snapshots should be used as a short-term rollback solution and should not be used for traditional backup purposes. See here for a brief explanation.

I did exactly what you said. Each night, I shut down the VMs, then do an export and restart the VMs. Then I copy the exports to some other physical location. This is a powershell script that is scheduled with Windows scheduler. The only drawback is that you have to shut down while exporting - which is not always acceptable.