Groove actually still exists, though it's gone through a bunch of branding and strategy contortions:
Groove 2006 -> Microsoft Office Groove 2007 -> SharePoint Workspace 2010 -> SkyDrive Pro -> OneDrive for Business (the current product)
Groove 2006 -> Microsoft Office Groove 2007 -> SharePoint Workspace 2010 -> SkyDrive Pro -> OneDrive for Business (the current product)
"When did the first sync web sites start coming out? 1999? There were a million versions. xdrive, mydrive, idrive, youdrive, wealldrive for ice cream. Nobody cared then and nobody cares now, because synchronizing files is just not a killer application. I'm sorry. It seems like it should be. But it's not."