I'd get annoyed if he phoned me at 3am and asked why i was quiet...but i have little comprehension of anything in the mornings.
I always kept my phone on vibrate under my pillow, and i still do that now infact, just incase anyone needs me at night...i dont know why I still do it...its been a while since anyone called/texted me then (Thank God.)
He was terrified of me leaving him, and so he was quite clingy, and if i wasn't online or something for a few minutes he'd call me and he'd always call my friends if i forgot my phone because he thought i was ignoring him and stuff. But that was just his paranoia and you just learn to live with it.
At that time I was feeling pretty unloved aswel, so to have someone who clinged to me, and felt that I was worth something was good actually, so it worked both ways in our relationship.
If you have a guy who cares enough about you, he won't mind you being depressed and needing him. I'm an EXTREMELY happy person, I don't know why but it takes a LOT to bring me down. So I figured that I may aswel give him some of my happiness and he gives me some of his depression to neturalise me.