Good old Google Chrome. It's the browser I'm using to write this right now. Unfortunately, I have to open tabs manually across all of my computers and that's quite annoying. However, I no longer have to as in the latest Google Chrome beta, it includes a new feature which syncs your tabs across all of your Chrome installs.
The feature doesn't actually keep the same tabs open across computers. Instead it adds an "Other Devices" menu on the new tab page in which you can select a tab from another computer or even Android device. And it doesn't just come with the single tab--it brings the full history of the tab so that you can go backwards.
There's no word when this will be available in the regular Chrome release, but you can check it out in the developer channel here.