I try and make good content first, then I ask for friends, family, and twitter followers to look at my stuff. They watch my stuff and at the end I ask for their likes, subs, and shares. But I have to say this, I have a couple of YouTube big guys in my niche and when they swing by and leave a comment my subs go up for 2 or 3 days and that's awesome of them. Why do they do it? Because I like their stuff and commented on their videos. Plus, they are nice people. I did not ask them to "please check out my video" either. I wasn't trying to get noticed, I commented because they're stuff was awesome and I respected what they were doing. So you might want to make sure you add to conversations of people doing cool stuff like. Now, don't be all super fanboy or stalky with it.
Summary
I ask friends, family, pinterest and twitter followers to look at my stuff
If they stick around to the end of the video I ask them to sub, like, and subscribe
I comment on "big guys" YouTube channels if I'm diggin their stuff, but I never ask them to do anything, if I become a real member of their community they MIGHT check me out
If someone big watches your videos/comments your subs will go up for several days