Should I mention the fact that I am a father?

I would not necessarily claim it as one of those when listing things on your application (I think it is a bit off scope). However, that does not mean that you cannot focus on what this has meant to you. Organization? Multi-tasking? Responsibility? All important skills for the business world.

One thing you might consider doing is trying to get involved in some things that you can include your child in and also give back to your community.

How old is your child. Maybe have a few suggestions with some more detail.

He just turned 2. Where could I pull that in? perhaps teh optional essay?

I would also say watch out for this when applying to schools such as Harvard and Stanford, who are known to now favor younger candidates. They're seemingly worried about their 100 2+2 students and other traditional students (out of Consulting or i-banking after just 2-4yrs of WE) meshing with older candidates. Even if you're "young" (25-28) by b-school standards, stating that you're also a father may hurt to an extent in how well they perceive you to relate to other students. It's not stated anywhere, but it's probably true.

In addition, they may worry about the "contribution" to their b-school issue. They know, and even you know, that being a father is not going to give you as much time to make the b-school a better place compared to those who aren't parents yet.

I would say only mention it if you have an AMAZING story about it, because they'll still make room for you if there is, otherwise, with Harvard and Stanford, I think it may hurt your chances.

Schools whose median age is higher would be where I'd feel more comfortable revealing fatherhood.