My wife has only one meaningful ex, since she and I met at 19. Over the years we've actually become close friends with the ex and his wife, attending each other's weddings, going camping together, and the like.
I'm comfortable with this because it's crystal clear that there is zero chance of anything ever happening between them again. My wife has unloaded enough on him over the years that it's clear the break was somewhat nasty and she'd never go back to him again. I'm sure the fact that they broke up 12 years ago, that the ex now lives many hundreds of miles away and is happily married with child, and that we see them only twice a year at most also helps.
I think a lot of concern about exes is focused on the unknown of physical attraction between two other people ... a fear lingers that there may be some kind of powerful chemistry that will bring them irresistibly back together. It's shallow of me, but I feel secure about this because the ex knows I'm far better endowed and is somewhat cowed by that, and my wife has really grown to like my size in our years together and has told me that he was lousy in bed. Nothing to fear there, as far as I can tell.
So yeah, it's possible to be comfortable -- even friendly -- with your S.O.'s ex, but only if you're pretty sure he/she has moved on and would never look back. I think ultimately the burden is on the partner who wants to maintain ties to an ex to demonstrate convincingly to a new S.O. that there is no threat whatsoever.
Steve