I think that many revolutions started because the population could convince the military to be on their side. What's your opinion on this? Does convincing the military play a big role in revolutions to get started?
Are there any movements in western countries where the military advocates more power to the people instead of their government?
The military is not a uniform
The military is not a uniform category of course. The Bolsheviks agitated among the rank and file for democratic and trade union rights in the military, iirc. Russian soldiers fought for the right to elect and recall officers and for an end to the death penalty among other things.
On the other side you have the tactics of those who mythologize the Bolshevik revolution, and attempt to convince junior officers in the military to support socialism, as a *sole* means to build revolution (*cough*, trotskyists, maoists, etc.*cough*).
The socialist position is that the rank and file are workers who need to be organized and united with non-military workers; they have to refuse to prosecute the war effort or crush strikes etc.
And more recently in history
And more recently in history try at least the introductory sections of this useful book;
http://libcom.org/library/portugal-impossible-revolution-phil-mailer