When i really like someone on the internet, i tend to give out surprise gifts like this (or this http://i.imgur.com/2kLyL.png) that are hidden deep in comment sections on Deviantart.

I also reply to picture messages with picture messages.
I believe artists that refuse to offer any sort of free drawings aren't worthy of their title. Even if its doodles, or full color masterpieces, i believe they have to have something free.