You can try switching to Whitehat Security's Aviator browser if you're a home user. If you're working in a business, you may try and present it to management as an option. Another alternative is to run a local squid proxy to intercept between a site and a browser. Doing so would enable you to use something like White Trash that works to minimize the amount of garbage sites making their way from the Internet, to your browser.
The biggest hurdle you will face, is one of what is akin to an "arms race" where attackers are constantly trying to weaponize an exploit to disaffect someone browsing. There is little you can do against some exploits/attacks given that most attacks aren't even patched until they are problematic (someone detects something odd). The work around would be vigilance in watching where your connections are coming from, and going to. You could try blacklisting known bad addresses, but this too becomes cumbersome when blacklists can easily run into the thousands.
There are also some low level options like modifying your user-agent as certain types of malware have the capabilities of detecting what browser you're using, in order to use the right exploit against you. E.g.: "if user == IE ; then send IE_exploit ; fi" So theoretically, if you're using say Firefox, with the user-agent of IE, a targeted exploit would fail.
When all is said and done, I always state that these attacks (browser based) are a law of averages. As an attacker, I would create exploits targeting browsers in this order: IE, Firefox, Chrome, Safari, Opera." The reason is simple, this is what I perceive to be in the highest pecking order. (I would get more bang for my buck). With that as a theory, the likelihood of someone targeting say Aviator is low. And if all else fails, you could use a text based browser such as lynx/links which do not run any kind of application/scripts (Flash, Java, etc.)