Uh oh... someone asked a question about vampires. Robbie you just woke the "monster" in me. LOL!
Vampires in literature (and I could movies and TV shows as some kind of literature as well) has always been one of my main interests. I wrote my final thesis for my A- levels on Dracula (and Frankenstein), did a seminar on gothic novels at university and um... yeah... I consider myself an expert.

Unfortuantely there's no straight answer to your question. Because vampires are such a popular genre, there are a lot of variations. Every author tries to be "different", set a different set of rules for his/her vampires. Sometimes sunlight kills them, sometimes they sparkle.

Some are allergic to garlic, some aren't. Same with crosses. Some sleep in coffins, some sleep in beds. Some are also shape-shifters, some stay in the same shape and body since the day they were turned. Well, you get the picture.
So an important part of every vampire story is to explain the rules and kinda make fun of some other rules that are commonly known about vampires. Like "what? Afraid of garlic? Haha, that's just the legend. I happen to love garlic pizza!"
Of course sometimes the rules are the same because there are only so many variations of the same theme and then authors influence each other and copy their predecessors. (which - imho - is not necessarily a bad thing)
So about the baby thing... and I assume you mean making babies in the "traditional", human way and not turning a baby into a baby-vampire: basic line: Some can, some can't.
The Anne Rice vampires can't even have sex - as far as I remember. The vampires in the Sookie Stackhouse novels can have sex but not make or have babies. In Twilight they can have both (sex and babies) - but the latter only if one partner is human.
It's pretty much up to the author what he/she wants/ needs for their story.
In the "classic" novels like Dracula, there's - of course - no mention of sex (not directly anyway) but the the final chapter of the book mentions Mina's son, so some like to interpret this as a sign that Mina's child is actually Dracula's.
I think most of the time vampires can't have/make babies since their bodies are dead and unable to "function" in the normal, human way.
*takes a deep breath*
Do you want me to go one?