As far as actual “exploits”, a lot of the tools-of-the-trade of teenage crackers, which consist basically of reverse-engineering a handful of relatively simple cracks that they pass around through whatever the forum of the day is (plus the obligatory passing around of bomb-making textfiles), are still pretty effective. When I was playing around with that stuff in the mid-90s it was pretty easy to get shell accounts on US military servers (prized so you could go on IRC with an army.mil hostname) by digging around for common Perl-script programming errors involving failure to sanitize inputs for shell metacharacters. I wouldn’t be surprised if you can still do something comparable these days. An increasing share of effort these days is also directed at cracking hardware devices instead of breaking into servers—there’s a pretty impressive steady stream of people, many of them teenagers, cracking Apple products, DVD encryption standards, and so on.