There was a post by Leonard Cassuto on having kids in graduate school and what a difference it made to one student when she heard that it was explicitly all right. The point that Leonard made was that our role as faculty is to support and educate our students and help them grow into the next generation’s leaders. This means listening to them. It means making it clear that there are boundaries. One of these is on their decision to have children.
Adorable Jacorri, born when his mom was in grad school.
I suppose there are people out there that secretly hope their grad students and postdocs will not have kids. Maybe these people think if they don’t talk about it, it will never occur to their group that having kids is an option. Isn’t that silly?
Obviously whether or not to have kids and when to have them is a personal decision. It is also one worth mulling over. Part of that may be discussing it informally with your lab friends. It should not be taboo. We talk about everything else at lunch, so why not this? I bring it up first. I think people should have kids when that feels like the most wonderful thing to do. I also think it can be a relief to have the first baby if you want to have kids. It puts all the anxiety of when it is a good time behind you. It turns out right now is a wonderful time.
Anna and Danny survived being born before tenure!
Obviously a family takes time. But can also give you balance and happiness, perhaps more than you ever thought one heart could hold. A number of my graduate students have had children in graduate school. Never has it been any kind of problem. In fact, it can really focus a student.
Me and my youngest Philip Queller, the only one born after tenure.
What I tell my friends and students is that I think having kids and having a career is completely possible. One can even enrich the other. But kids take time, so something has to change. That is most likely to be in the hobbies, free time, hanging out department. Instead you will find ways to exercise, socialize, and cook dinner that involve those sticky little curious hands.
My own story is that my daughter was born the month I started as assistant professor at Rice. Her brothers came 3 and 10 years later, each a welcome, joyous addition to our family. If a paper or two was missed, or a seminar trip didn’t get made, it mattered not at all. Perhaps thinking harder about what work was worth doing made me a better scientist! So have those babies if it suits you. We will welcome them and help you fit your new life together!
Sociobiology 
Our son was born when I was a postdoc and my husband was a PhD student. I try to tell that story to grad students and postdocs around me (from my lab but also others, in case they did not get the positive side from their own advisor) as often as I can.
I’m a grad school baby myself (born in my father’s second year of grad school), and now I’m also a grad student facing something that same question. I’m now married and we are considering having a child after I finish my coursework and get my research proposal approved. Luckily, my university is incredibly supportive, and they even organized a lecture to the women in the department on how to deal with balancing family life and an academic career.