Netscape -> IE -> Neoplanet -> Maxthon -> Mozilla -> Opera -> Firefox -> Chrome
Neoplanet was more like an IE shell but I'm listing it anyway
I've also played around with Flock but never really got into it. It felt a lot like that MSN Browser Microsoft was trying to push back in the day.
There was a lot of jumping back and forth between Opera and Firefox for me. It was mainly a battle to see which could handle and retain my bookmarks more reliably and across multiple platforms, eventually Chrome showed up and won. Opera fell out because it slowly became strange to me, the way it scrolls pages felt weird and out-of-sync, it was more of a preference thing. I had varying reasons for leaving Firefox.
Initially, I hated Chrome. It was bulky, ugly, and hogged a lot of resources unnecessarily, and it was not customizable at all. In time, it was refined and took over as my default.
Firefox I always loved because how customizable it is; it gave me a lot of liberty in managing its appearance and its functionality, however, I learned the hard way that you can't truly rely on 3rd party plugins to back up bookmarks. Xmarks worked really well for a while but one time, when I was uninstalling Firefox, I selected to remove Firefox completely and and apparently since the bookmarks were synced with Xmarks everything got deleted from the cloud too. It was kinda counter-intuitive but lesson learned. By the time Firefox had implemented FirefoxSync, it was too late. I had already moved on and Chrome had slimmed down its interface to the bare essentials (just the way I like it).
EDIT:
Amended with -> instead of > in agreement with Cobra