You can create a free favicon online , ofcourse you have many choices , but the best way i prefer is to favicon.cc , i myself use it , it offers creating of favicons online for free , with no cost and at the same time , you can also spread your favicons all over the world by publishing it under a free and open license , everything is easy , all you need to do is to just have a piece of art , it also enables creation of transparent favicons and also animated ones.
Click here to go to favicon.cc
Click here to go to favicon.cc