How often does this happen?

It happens a lot, don't know the exact figure, if there is one - I assume it happens just as often as often divorces do, and that's over 50%.

Though, It's not so much that it may "looks bad on the kids" because it really won't because so many have been divorced and remarried. But, if it happens often, or even once and the kids were close to the first husband, most likely their dad, or feels like their dad, it may very much affect the kids emotionally (most will not show it either). Kids get attached to the men in their mother's lives, especially if they don't have a good relationship with their own father or have a good father figure in their lives, will get hurt when the relationship is broken up because they don't get to see that person any longer. That's why, even if just dating someone while you have children, you should make sure (even though it's hard to predict it will last or not) that the relationship is for the long term for the very reason the children become attached to this person too and can and does affect them emotionally. They suffer a loss too. It can affect their self esteem, school work, social skills, which can last into adulthood where they have difficultly forming lasting and healthy relationships.

I would have a talk with the children, and let them know YOU love them, and they are more important than anyone. Also, the other man, who is not their father, has to respect that he is not their father, but be kind, helpful and respectful or the children's health, emotional and physical, and be a special person in the children's lives. It would "look bad on them" at all. Anyway it doesn't matter what "looks" bad, but IS bad. Many children come from broken homes and have step-fathers and biological fathers still in their lives and do just fine, after the initial hurt. The need to be able to talk about it. Again, it is a loss for them too, just as it is for the one who was left for someone else.

Also, this depends on the age of the children too. The older, the better ability to get over it. Which is the reverse for many other changes in their lives.

hard for the kids especially if they are close to their step-dad, if their step-dad was the only real dad they've known.

yes