@ MrPete:
Well from what I recall, Vampires were depicted as a self-aware endangered species. In the plot, at some point in the past, when Vampirism became widely known to the humans, a massive religion inspired holocaust nearly drove them to extinction.
The ancient ones are smart enough to know that they have to live in the shadows and be careful about their numbers. And creating a lot of young and reckless vampires will only betray their existence to the world, as young inexperienced ones who have just tasted immortality and super-human ability are impossible to control or educate en masse. So they had to prune all new converts and over time leave only a few of them (who show mental maturity and restraint) alive to join the ranks.
There is one interesting element they didn’t exploit, which is the possible role vampires played in the Renaissance and the popularisation of science in helping debunk public belief in Vampires.

@ Dileep:
This is a nice take on it. If you have to survive several hundreds (or even just a hundred) years in order to be able to create another vampire survival of the least obvious raises its head.
Do you remember if old vampires automatically create offspring once the ability manifests?

I can’t recall where I’ve seen this, but there exists a Vampire mythos where fresh converts cannot transform their victims into Vampires, but ancient (read centuries old) ones can. Its as if even Vampires have to undergo a puberty period (which could take hundreds of years) before they can reproduce. Given the selection pressures from internal conflicts, human Vampire-Hunters and the Sun, this also seems to ensure that only the best “Vampire-traits/genes/essense” survives the coming eras.

The idea of vampires being able to “take a bit” from their victims and thus causing an addiction is also found in the RPG Shadowrun and to an extent in the World of Darkness – Vampire.
In the WoD vampires can take blood from their victims until they die. If they stop before that point the victim will recover (but may need medical attention depending on how much blood was taken).
In both systems a vampire has to drain a victim of blood (or Essence in SR) and then give some of “his” blood/essence back in order to create a new vampire.

I quite like this system since it gives the vampire control about whom they turn into a new undead curse to mankind and doesn’t create a plague that decimates the humans in years (which would make RPGs dealing with “being a vampire” rather shortlived without the chance to span centuries)
In movies on the other hand the infectious variant is a good sign for more action…

the original bram stoker novel teaches us that a victim has to die in order to become a vampire. if you just sip a little bit then and now he would survive and “only” become submissive.

A german pulp series around the year 2000 called “Vampira” had a more sophisticated concept of vampires and reproduction. I liked it very much, but it ceased after around 130 parts when they started to involve Cthulhu, and the readers didn’t like that very much (me neither, it simply didn’t fit into the history).

The idea was a very nice one:
the first vampires were only 20, and they were the children of Adam and Lilith (who came before Eva). Lilith was a powerful witch and sent their children to the future to hide them. But of course God saw everything and so she was damned to eternal imprisonment because she gave life to vampires, and Adam and Eva started afresh ;).
The future the vampires were sent to was Uruk in ancient Mesopotamia, and they declared themselves “gods”. This was the real reason why God then sent the flood …
Similar to Noah’s ark there was a “vampire ark” to save the vampire “gods” from the flood.
During the flood they somehow lost most of their memory. They decided to sleep centuries, where only one of them would stay awake to guard and try to find out about the lost memory, changing places after each century. In this time the guard created “normal” vampires by having small babies drink his vampire blood from a magic goblet (this only works with the guard’s blood). Normal vampires can only create stupid and powerless vampire slaves which have a limited lifetime and decay after some months.
The main protagonist is the daughter of a human and a vampire, and ancient Lilith from her prison had planned to have her extinguish all existing vampires, then travel back in time to free her and ask for forgiveness.
This was a remarkable pulp series, imho the only one where God is really a part of the story and is doing things.
Sorry, only a german Wikipedia link available:
http://de.wikipedia.org/wiki/Vampira_%28Romanserie%29