Interesting post today on Jezebel about being friend-dumped by an ex because his new girlfriend tells you too. I am conflicted on this issue, mostly because I've been on both sides of it, in a manner of speaking anyhow. I'm pretty sure that none of my exes have ever been forbidden to talk to me by a new girlfriend, though I could be wrong.
The problem I have is when girls who are dating guy friends who you've never been involved with get jealous and beat them (emotionally) into limiting contact with you. A former friend of mine had a crush on me once upon a time. I was aware of said crush and was careful not to encourage it as the feelings were not returned. He eventually got a new girlfriend who I thought was cool for a while. One day my friend did me a favor by picking up my cat from a friend's house when I was super sick, and his girlfriend got super insecure and jealous, thinking that if he would go out of his way to do me a favor he must still have those feelings for me, etc. etc., and he stopped talking to me. It was all super lame and I roll my eyes at the stupid insecure girl for it.
On the other hand, I am generally unhappy when I hear about my current boyfriends interacting with their exes. If they had normal exes, it wouldn't be a problem, but most of these girls seem to be emotionally needy and a little unbalanced. I was chatting with a friend about this and I mentioned that I don't want them taking his emotional energy, that's for me! He told me I was being unreasonable and he compared it to being upset when he spends his money taking a friend out to dinner because he's supposed to be buying dinner for me.
I said that wouldn't be unreasonable if he was taking his friend out to Alexander's for kobe steak every week for no special occasion and paying say because his friend was broke. He would be using money and applying it frivolously toward something that isn't bringing any real rewards. Whenever crazy-ex-girl calls the guy I'm with up and goes on and on about her personal problems with him, he's spending his emotional energy dealing with it when this friendship doesn't have any real upsides.
However, I'm not really an iron fist type, I would never forbid my significant other a friendship or dictate who they can speak to. I generally try to keep the majority of my unhappiness about it to myself (not always succeeding) and trust that it will eventually work itself out and crazy will go away and find someone else's shoulder to cry on. And that usually happens.
As for my own relationships, I don't do friendships with exes. It's not worth it.