well this is in the wrong section but it's ok ur new. what do you mean you want an art application or you want an art application to create an app? i don't understand. anyway a good free drawing program in sketchbook pro . there is a free version of it. i think it's called sketchbook pro express.
Gimp is pretty good for raster (bitmap) work. 3D Art- Blender works really well. Vector Art- Inkscape is an awesome tool. I have actually started using this as my primary vector art tool. All three of these work well as portable apps too (meaning no install, run them from a flashdrive). http://portableapps.com/apps
I agree with Flickitty. They are all awlsum and stuff. Inkscape is a great vector tool and is one of the best opensource projects out there. I use Inkscape and Gimp in tandem for all of my 2D art. Blender takes a bit of getting used to, but it works. Lots of good tutorials out there on the interwebs.
