I do them! Check out this journal for pricing details! If it's a cartoon I like and have seen, I'll be able to whip up something for you! I like to consider myself a pretty good mimic-er of different styles when I put forth the effort.
Examples of Cartoons I'm known to draw/have drawn (even if not displayed in my dA gallery):
My Little Pony
Regulations: If I think a request is out of bounds, I won't draw/write it, but I may offer a suggestion on what could make it more geared to what I'm okay with doing. If you're not sure about something, ask away!
I don't do free requests unless they're for voice-acting.
Other Places I Lurk
I also have Skype. If I know you fairly well and you'd like to IM me, let me know! I like to rp, but please don't add me if that's the only thing you ever want to do or talk about.