Do I need to back up the log file drive when using VSS snapshots in simple mode? We're currently using AppAssure to back up the SQL servers (2012/2014). It uses VSS snapshots. All databases are in simple recovery mode. Do I need to bother backing up the drive that contains the ldf files or is it enough to just back up the mdf files and let the log files recreate during a full restore?

SQL Writer Service explains how VSS can be used to take application consistent snapshot backups of the database files directly. It says it does not support log backups, which is why I asked this question.

Snapshot Backups are a feature of SQL server that allow hot backups without doing traditional dumps.
Couple thoughts on this one:
Do you have more than one database per-SQL instance?  Are they all "owned" by the same application?  If you've got multiple DBs for multiple apps, can your backup solution only restore ONE database (both the MDF and LDF) or will you have to restore all the DBs?

As Kris G pointed out, how do you KNOW your VSS snapshots are restorable to a working SQL DB?  Have you test restored them somewhere?

Lastly, to cover your question, it's a bad idea to not backup the transaction log.  Even in Simple Recovery, you can have "in flight" transactions that haven't gotten to the point of being written into the MDF yet.  Not having the Trans Log when you restore one of these will make getting the DB back online and functional a much more difficult task.

Frankly, I'd take the safe way out, turn off the VSS snapshots of your SQL data and log drives, set up a backup process using the native SQL backup command on a set schedule to a location that is covered by the VSS.  More work for you, a bit more work for whoever's in charge of the VSS snapshots, but you'll be much happier if / when you have to restore a database down the road.