Yes, and they are quite common, they are called aftershocks.
An earthquake redistributes the stress that creates the quake across the fault line, which then creates new points of stress, which result in additional earthquakes, which further redistribute the stress again, and so on and so forth until all the energy is spent.
Earthquake swarms also exist. They basically work on the same principle as aftershocks but are much stronger. They tend to occur in places where you have many faults in the same region. The release of pressure on one fault causes movement that puts more stress on other faults, causing a cascade of quakes. California and other transform faults are famous for them. Here is rather nice BBC film about them. http://www.dailymotion.com/video/x2262rz_bbc-horizon-2003-earthquake-storms_shortfilms.