Webservice Logs

Not that I know of.  I end up having to RDP to my servers occasionally and look for sites that have grown inordinately, then look to see if it's those log files - then nuke them.  You would need to delete them via FTP if you are on shared hosting.

You can simply update your QB Add-On to the latest version. The instructions that come with the update explain how to purge the logs.  The latest version has logging turned off by default.  Alternatively you can open the file "Quickbooks/webservice/Web.Config" and set "True" to "False" next to logging.  That works with all versions.  If your db is collecting a lot of data it is probably because you run Web Connector on a schedule (e.g. every 15 minutes).  Unless you need real-time inventory synchronization you should only run it once per day to once per week.  You can also run it manually just before you need to work in QuickBooks.

Yes, I am referring to the ProductCart Synchronizer for QuickBooks.  The support console and logs are two separate features.  Good question! So you can use the support console after logging is turned off.  You are running the latest version.  If you still have logs then you may have missed a few steps when updating. You can read over the steps again here.  Since you use real-time synchronization you may periodically want to purge the tables Greg mentioned above.  They will be added to the "Clean-Up Tool" in the next version.