it depends...on the situation.
My DH's ex wife and I have run the gamut of the friendship relationship. For a while, we were pretty friendly. Not sleepover, cry on my shoulder kind of friend, but we'd chat on the phone now and then for a bit and I'd be in email contact/phone contact with her pretty regularly about scheduling, plans for our weekends with the girls, etc.
Then for a bit, she met/married/moved in with a man very quick (3 weeks, and wanted to change school districts etc), and it was hard for me to accept that her choice. It came apparent that my opinion didn't matter, to her, my DH or anyone else for that matter. That was also when her attitude to me and DH started to change. She, because of the friendly relationship between us felt ok knocking my husband for his past failures, and his family as well...the kind of joking that you would do with a friend, which made me feel uncomfortable.
So, I went into a period of time when I wouldn't talk or email her. This also had ALOT to do with the fact that I was feeling taken advantage of by everyone in this dynamic and felt that Tracy (the ex) and my DH needed to be communicating to each other, and it wasn't MY job to make sure that the skids had enough time with their dad, or make plans, schedules, do their laundry etc. There was also a time when DH was away that she and I made plans to get the kids together to play, and she completely blew me off, never called....and that hurt.
Now, we are at a comfortable place. I call/email if I need to: for example, this weekend we wanted to take the kids sledding, I called to ask her to pack snowpants and boots, as Dh was at a conf and wasn't sure if he was able to contact her. I pass along my DD's nice hand-me downs to the skids, but will call/email to see if they are something she would like. I called her when I caught my DD using SD6's webkins account when the skids weren't here, just to let her know and prevent drama.
In that long post, I guess every relationship is different, and it takes some trial and error to find what are comfortable boundaries for everyone. Early in the relationship btw DH and I, I wanted to be super involved. Now, I think we are in a better spot.