Kate Beaton is a Canadian cartoonist best know for history comics and Canadian comics. But she's also tackled this important question. Her Mystery Solving Teens have "taken on" several cases. I've failed to tell you before because, well, you know, I should maybe write a blogpost about every comic on the web I like? It doesn't say "Webcomic Review" at the top of the page or anything. But I've been broken out of my apathy by the introduction of a new character, Vanessa the Girl Reporter. Being part of the Mystery-Solving-Teen-verse her self published "newspaper" is called "The Shit Talker" and - look just read the whole series okay? Work Warning: there's some swearing because, you know, they're those sort of Teens, right? Anyway if your work is cool with you looking at webcomics, I don't see why they should get uptight about a bit of profanity but then that's why I'm not your boss.
The Docks Mystery.
The Ghost in the Library.
The Snow Mystery.
The Principal's Office.
Boy Detectives, Girl Reporter. (Be sure to check out the sketches below this one).
Some other Kate Beaton stuff I like: A bunch of comics, Charlie and the Turnip Factory, Sexy Batman. Or maybe just read her whole site! It's not like you were going to get any work done today.
For actual mystery solving non-teen* comics, may I suggest John Allison's Bad Machinery.
* They're tweens. I cringe writing that word.