Please heeeelp me I've been searching for this cartoon for like ages and I still can't find it.All I remember is this brown haired little girl with bangs and hair tied at the sides who was called Penny!
I would be greatfull if anyone could help!

Your description reminds of Pippy Longstocking but she had red hair.

When was this cartoon on TV?

Oh no its not Pippy Longstocking.I'm not quite sure about the exact year but it should be in the 90s when I was a kid.

Nobody knows it its like I imagined it! :)

"Inspector Gadget", perhaps?

I agree with Tallyman - Penny, with her dog 'Brain'
Here's the intro:
http://www.youtube.com/watch?v=e-JHfXVlkik

Unfortunately... nope!Now I am positive that I'm never going to find it!!

Darn, I thought Tallyman had it! If it's not from inspector gadget, maybe you're thinking of The Rescuers? (the first one) The main character was a little girl named Penny, with bangs and pigtails, here's a picture:
Google Image Result for http://fc05.deviantart.net/fs71/i/2010/108/c/e/Penny_and_Rufus___the_Rescuers_by_Felandrim.jpg (http://www.google.com/imgres?q=the+rescuers+pictures&hl=en&sa=X&rls=com.microsoft:en-us:IE-SearchBox&rlz=1I7RNWE_en&biw=1024&bih=548&tbm=isch&prmd=imvns&tbnid=NU0bS9M9-SwFFM:&imgrefurl=http://felandrim.deviantart.com/art/Penny-and-Rufus-the-Rescuers-161134809&docid=9D_oBpKGClqF5M&imgurl=http://fc05.deviantart.net/fs71/i/2010/108/c/e/Penny_and_Rufus___the_Rescuers_by_Felandrim.jpg&w=900&h=653&ei=vvfgT5uWDKGU2AWW7vzNCw&zoom=1&iact=hc&vpx=532&vpy=134&dur=766&hovh=191&hovw=264&tx=167&ty=142&sig=101324136229240512383&page=3&tbnh=164&tbnw=194&start=20&ndsp=13&ved=1t:429,r:11,s:20,i:177)

Noooooooooo.Maybe I shouldn't have asked!! I thought that because I found : (Raggedy Ann & Andy: A Musical Adventure) here , I would find this one too!! :(
As it turns out I actually imagined it and even worse I have apparently convinced my mother and brother that it exists..

Was it penny crayon? I've been thinking for ages about a cartoon I used to watch and then it suddenly just clicked penny crayon!!