I've been using Opera as my main browser since 2000. I absolutely love it. It's fast, reliable, customizable and has almost never been found to have any security flaws (although on the rare occasions it has, they've been patched within three days or less). Before Opera I was a Netscape loyalist, but Netscape got to crashing more and more often and even when it didn't bring the whole system down with it, I had to reboot anyway in order to get Netscape running again.
I am using Thunderbird for e-mail though, because Opera's e-mail client absolutely sucks.
And AFAIK Opera doesn't use any Mozilla code. In fact I believe Opera has been around since before Mozilla was available seperately from Netscape.