How do you get multiple rows of tabs in Google Chrome?

In short, you can't, and it doesn't seem to be coming. I'm guessing they're trying to teach you good tab management and to let make you play with the tab ripping. There are many alternative solutions to tab overload though. Take a look at TooManyTabs.

Take a look at TabsOutliner extension. It gives you editable overview of all the windows and tabs in Chrome. Here is a screenshot:

A work around would be to use pin tabs. If you right click a tab and choose pin it will become a small button to the very left. Also, it'll stay there when you close your browser and open it again.

Doesn't solve the problem but you'll at least get a better overview of your tabs