Using any sort of "Java or other active content Enabled Browser [active content]" is a potential security risk, in less serious cases your IP address can be extracted using javascript giving a potential cracker an address to start snooping around, but to come across this problem you would have to visit a webpage with the maliciuos code in it. unfortunatly a hacker can break into a web Site like Microsofts or Yahoo and plant the malicious code.
Looking about the browser security settings it seams the only way to stop Malicious active content is to switch of Active Content
So you can see the potential, but you've got to think in the context of acceptable risk. As for why IE and Netscape are popular is that they are usually given awayfree on magazine Cover CD's an they tend to support the most "features". Personally I use Internet Explorer, despite my distain for microsoft products, as it the web is a bit more IE friendly than Netscape friendly.
As for security examples can't think of any but try going to a couple of hacker sites and look under sections marked as "Exploits" or similar you may find some info on current techniques, a good place to start is www.lopht.com.