Should you ever message a girl first?

I guess if a girl really likes you and is interested then they will show signs of interest and message you first?

I have no problems with messaging first on dating websites and over Facebook but i was thinking is it an affective way to create attraction?

Surely a conversation will flow better if they message first after being attracted to you

I want your guys options on who should message first and why and should you message girls you've only spoken to one or two times?