Energy vampires were chasing me. They looked somewhat like the Wraith from Stargate: Atlantis. They cocooned their victims and drained their energy over days eventually leaving them as withered shells. I eventually had them follow me into an android factory in Japan and had them "feed" on an army of these:
Which had the effect of electrocuting the vampires. Unlike all the horror movies, I didn't check to make sure they were dead, I just ran! I don't care if they are still alive, I am and would like to remain that way. The monster always grabs the checker and kills them! (As my dad always says, "That's in the script. They need another twenty minutes of the hero being chased to fit a normal movie length.") Self preservation is a great motivator!
I'm sure my thyroid issues were to blame for this dream's plot. For the vampires, I blame my crush on Joe Flanagan!