Actually I stuck with Mozilla until this month. So far the latest versions of Firefox and Thunderbird hasn't cause me any problems.
Mozilla only caused problem on my older PC which is on 24x7. When I keep the same instance of mozilla running for more than a day or so it sometimes becomes unresponsive and I have to shutdown the process and restart.
I do remember having more serious problems with earlier versions of Mozilla, but it was worth it everytime I scanned for viruses and spyware and only find cookies.
I have only used Opera for testing when I work on web pages, but it seems like a great browser.