The Internet Storm Center shares some recent links that ALL BROWSERS have issues. I can see this as a browser is simply a tool that brings back objects from a web site.

Internet Storm Center - Browser vulnerability Day
http://isc.sans.org//diary.php?date=2004-10-20

While FF and Opera are rated as safer than IE currently, I wouldn't rest on that alone. For example, Secunia documents brand new tabular browser vulnerabilities for both FF and Opera.

TABULAR BROWSER VULNERABILTIES
Firefox, Opera, Safari, Konqueror
http://secunia.com/advisories/12713/
http://secunia.com/advisories/12712/
http://secunia.com/advisories/12706/
http://secunia.com/advisories/12892/

NEW HIGHLY CRITICAL IE VULNERABILITY
http-equiv
http://secunia.com/advisories/12889/

Keeping Windows patched, your AV protection updated, a good Firewall, ramping up IE or other browser security settings, and thinking before you click are all imperative for the user community.