I have my therapist's cell phone number, and he's never told me that I can't text him. But aside from scheduling issues, I've only texted him twice--once on a Friday afternoon and again the next day (saturday afternoon). It was when
I figured it was enough of an emergency to be justifiable. I would never text him in the middle of the night though. Even if the world was ending, I'm pretty sure I can wait till the next morning.
I've only emailed him three times. Once because I needed to reschedule a session, and the other two times I sent substantive emails after really difficult sessions where we basically got into fights. The first time was the week before Thanksgiving, and I wasn't going to see him the week of Thanksgiving and I just couldn't wait that long to talk about things.
The second time was the week before Christmas, and although we had a session scheduled the Thursday after Christmas, I was so distraught that I couldn't function so I wrote him.
I have to say that those two emails represent the most progress I've made in therapy so I'm glad he allows emails.
I really try to limit my between-session contact to times when I really really need it, and I don't think I'm creating too much of a burden for him. But I also really need to feel like he cares about me, and if he didn't allow outside contact at all ever, it would be really hard for me to believe that he cares.