I usually carry my phone with me everywhere. I've even answered the phone while sticking my head out of the shower on more than one occasion.
It's a really bad habit that I'm working on changing. One of my ENFP friends "trained" me to be that way but now that I don't think it is necessary to cater to her every beck and call (she was wasting a lot of my time and energy on social/her own personal drama) I no longer carry the thing with me as much as before.
And since I'm seeing someone, who happens to be an ENTJ, I pretty much know his schedule inside and out, so I do not call him when I know he is busy. When he is free to talk, I leave it as an open opportunity for either one of us to contact the other by carrying the phone with me.
I screen a lot of my calls, reject plenty by silencing the ringer, and return SMSes fairly quickly and dependably. I think I reject my Mother's (ESFJ) phone calls the most of anyone haha. I never, ever, pick up the house phone unless my Dad (ISTJ) and I are staring at each other, wondering who will have to pick it up first.
I am an ambiguous IxFJ.
edit: I am not afraid to talk on the phone whatsoever, it's just an inconvenience to talk to certain people when I know they have a difficult time ending conversations at inopportune moments. Usually, I just won't pick up the phone if I am busy anyway, so I don't have to worry about that as much.