I think it depends on the person. I have two exes I would never be friends with on Facebook and one who is not only my friend on Facebook, but also one of my closest friends. Our relationship ended on good terms (we decided we were too alike to be partners, but great as friends) and there's no potential that we would ever date each other again. So, in some circumstances, I think it can work. In others, it's just a bad idea.
I think this is more of an instance by instance question. I have some exs (mainly those from more recent years) that I wouldn't dream of adding. My middleschool sweatheart on the other hand has been my ff since I got a fb. My general rule of thumb, if I wouldn't hang out with them in person I won't add them on fb.
Wether or not I associate with people in everyday life (not online) depends on how my partner and I both feel about the particular person. If its someone either one of us thinks may attempt to cross boundries I normally stay away, this seems to follow through to fb as well.
If its someone who will respect your current relationship ( or if your single they respect the fact that you aren't with them) then I think its fairly harmless.
Unless of course its so one can spy on the ex in question because your not truly over a break up. That's a whole new can of unhealthy worms. exs are exs for a reason. Holding on won't help anybody get on with life.
I voted yes, but I suppose there are times when it might not be ok. But in general, I don't see a problem with being friends with an ex. In fact, I'm still quite close with an ex. We chat often.
If you think it's causing trouble in your new relationship, then it could be that you're still hung up on the ex, or it could be an issue of lack of trust or other issues with your new relationship. Very rarely is being friends with an ex the reason that a new relationship breaks up, in my opinion. If someone else can get between you two, then there were mostly likely issues to begin with.
Now, if the ex is bugging you all the time, or messaging inappropriate things or doing things you don't like, then un-friend them, obviously. But, a healthy friendship with good boundaries and a mutual respect, I don't see a problem with that. When you aren't with someone anymore, I don't see the need for them to vanish. So, it didn't work out. There could still be friendship potential there.
I think it is totally fine, because then you can talk to them eventually (once you are over eachother), I learn a lot from my ex's and stuff and it's fun to catch up. Although if they are annoying you you can like block them/ put them on your not talk to list or what not, but that causes less drama if you shared a bunch of friends.
I don't think that there's a general "this is okay or this isn't okay for everyone" on facebook. I think that it absolutely depends on the people, the dynamic, the terms upon which you are with your ex and possibly even other factors.
My SO has his exes and fb friends. I have one of my two exes as fb friends. I personally think it depends on the situation. I'm personally someone who can't handle having exes as facebook friends. For a long time at least. I honestly shouldn't have remained fb friends with the ex I'm currently fb friends with. I'm fine with it now, but it made the healing process a lot slower in the beginning. My SO appears to be alright with being fb friends with his exes, so more power to him.
One of my ex's is a good friend and is friends with my current partner and most of my social group, there's no problem! I'm not interested in being with him again anyways. I don't have any issue with my partner being friends with his ex's either!