It's not really a series. The games are made by different developers. Canal+ Multimedia developed the first two, which are in sequence and really should be considered one game: Dracula: Resurrection and The Last Sanctuary. In these two, you follow Jonathon Harker as he attempts to rescue his Mina from the clutches of the count. They are terrific and the graphics are still astonishing, IMO, especially in the cut scenes. Some of the puzzles were taxing (at least for me) but not enough to make you want to bite somebody yourself, and all fit perfectly in advancing the game.
The third game is by Kheops. Dracula 3: Path of the Dragon, follows Father Arno as he hunts down Dracula. It is the driest (in my opinion dreary), has a very different Dracula who appears very late in the game, and is my least favorite of the three.
Frogwares created a game called Dracula: Origin in which you follow Professor van Helsing as he chases Dracula through a cemetery in London, then to a strange monastery in Vienna, the sands of Egypt and last to his castle in Transylvania. This is a wonderful game, right up there with the first two but different in look and feel from Resurrection and Sanctuary, in which a sly (sometimes too obvious) sense of humor peeps through, though Dracula has a bit part in this one, too. Another game with beautiful graphics if you care about such things.
Frogwares made a follow-up casual game called Love Kills, available from Big Fish, that oddly shares the box art from the European version of Origin but is in no way to be compared to the adventure game of that name. It's pretty but not nearly on a par with it.
There are reviews of Dracula 3 and Origin here on GB in GB Reviews and some discussion of the first two in the Member Reviews from the forum. Go read and salivate if you're a Dracula fan and haven't played them.