What themes do Stoker's Dracula and Shelley's Frankenstein share?
As jakegabe28 has intimated, there are significant amounts of similarities between the two novels thematically.
The first is isolation and alienation. In Frankenstein the monster is isolated from his family and friends and alienated from the rest of society, from himself, and from the love of others. In Dracula Harker is isolated and alienated in the novel, at least quite significantly in the first two chapters.
Appearance and reality is another whopper of a theme that each share. in Dracula the Count is often shape-shifting and donning on disguises and ruses that he can manipulate reality with. In Frankenstein the monster looks hideous and evil, but is at first kind, lost and lonely. It is not until he finds out who is responsible for his existence does he begin to harbor hatred or gain a desire for revenge.
Duty and responsibility is another them we could discuss at length. In Frankenstein Victor takes responsibility for his creation and his creation's actions and seeks to right his perceived wrong by hunting the monster. In Dracula the band of good men gather together, take responsibility, and see the destruction of Dracula as their duty to mankind.
These are only three and rather brief treatments of each, I'll admit. There are many more...
Absolutely. I'll address one common theme because I'm sure you'll receive other answer, as well. One common theme would be the fascination with the abnormal, the different, the frightening. Society, in general, has always had a fascination with the macabre and with abnormal or different. Frankenstein is a creation that is horribly ugly and has superhuman strength. Because of his appearance, people are frightened by him, despite the fact that he is actually quite subdued and gentle at times. His appearance repels people, but there is also great interest in him. Dracula is also a frightening and intimidating figure, but in a different way. He is more human in appearance, but is surrounded by mystery. Also, woman are drawn to him in a very strange way. It is almost if he can cast a spell on them. Dracula does not have a naturally gentile personality, though, and is an "evil" character who murders people to sustain his own life and to turn others into the "undead."
Both were groundbreaking stories and each help set the standard for horror. Frankenstein was made near the end of the 18th Century, Dracula near the 19th.
Both deal with the theme of the Outsider. In Frankenstein, both Victor and the monster are outcasts. Victor in his driven obsession, the monster for its state of being. In Dracula, it is first Harker who is the outsider in Transylvania. The Count is more of a prescene in England than an actual character (despite what the films may portray), but the end shows the Van Helsing's group as strangers in a strange land. Great topic by the way.
Both stories are really great examples of gothic literature wth all the supporting devices: creepy setting, element of the supernatural, suspense.
On a deeper level, Dracula and Frankenstein are both unnatural creatures or subversions of nature that Shelley and Stoker manipulate as metaphors for humanity.
One common theme is free will versus determinism. Do we really get to choose who we become? Did Frankeinstein's monster get a choice? Did Dracula? How do we get to save ourselves from what we might become?