Hi N. - I have a Bob Dualie for my twin boys and we take it everywhere! It will fit through security, but as someone else mentioned, they will have to hand check it as it will not fit through the US scanners. We also gate check (just tell the person at the gate you need a tag). You will want to make sure everything is out of the basket, and additional cup holders, etc are taken off as it will make security faster and you won't lose anything when they put it under the plane. When gate checking, I collapse it but do not take the wheels off.
If you are going abroad, some international scanners will fit the Bob as they are designed for very large items. But, I have learned that some older cities have very narrow sidewalks that make it difficult to navigate.
Good luck!