Who knew you can do this with Google Chrome?
Look at the picture carefully notice the short tabs?
They are normal tabs that have been “pinned” (right click on a tab, and tell the browser to pin it). Pinning shortens them to an icon, and makes sure they do not resize when many other tabs are open.
The really awesome thing is that they get synched - so any machine you log into gets your pinned tabs pre-loaded too.