While Kenneth Branagh's movie aims for the adaptation of the actual book, and is basically a completely different story, it still uses some ideas and contains few small nods to the James Whale's 1931 movie.
The idea of grave robbing and using corpses was first made popular by the 1931 movie. Also, in both movies, a hanged man is used as one of the bodies. In Branagh's movie however, an additional twist is added, as the Creature is primarily created from a murderer and his victim. The fact that Victor uses a brain of his friend and a person he admired adds an extra dimension.
One of the most famous lines in history of cinema makes its appearance - "It's Alive!", although in Branagh's movie it's expressed as realization, when in Whale's movie it was a yell of triumph. Also, in both movies it's the electricity that is the key ingredient in bringing the Creature to life, however that might simply stem from the novel. In the novel, a "spark" is mentioned as well as galvanism (electrical stimulation of muscles)
In the novel, Victor starts working on a female companion for the Creature, but abandons his work before finishing. It was Whale's "Bride of Frankenstein" that first showed the Frankenstein character, here named Henry, to actually finish his work.