Why do flies indoors always fly around in circles? Isn't this aimless? SOmetimes a single fly, sometimes several flies go round and round and round- WHY?

Because the tower refuses to let them land with a full tank of gas.

I had hoped someone would know! Until we know, flies will have this secret over us, hehe.

I found the following at:http://answers.google.com/answers/threadview?id=96276
Summary The three-dimensional flight paths of male Fannia canicularis underneath prominent indoor landmarks were filmed and reconstructed for analysis. The flies patrol well-defined airspaces (of about 50x50 cm horizontal, 25 cm vertical extent) underneath landmarks like lampshades. Their flight paths have a distinct structure: they fly straight for on average 400 ms and an average distance of 20 cm; they change flight direction by abruptly turning through on average 95° and continue to fly straight. the sign of changes in flight direction is kept constant for periods of 2–20 s and changed at irregular intervals. Male flies approach a landmark from below and, in the absence of other flies, settle to patrol an airspace close to the landmark. A second male approaching the same landmark chases, or is chased away by, the patrolling fly when it comes too close and may eventually settle to patrol 10–30 cm below the airspace occupied by the first fly. A dummy fly presented to a patrolling fly between the airspace he patrols and the landmark is vigorously attacked from below and prevents the fly from regaining his former patrolling station. By trapping flies on sticky ribbons suspended from the ceiling, which served as landmarks, it can be shown that males and females approach and land on landmarks. It is suggested that male flies establish a lek-type mating assembly underneath landmarks to intercept approaching females. The position of male patrolling stations relative to the landmark suggests that females might arrive at landmarks from the side (and not from below, as males do), thus crossing the dorsal visual field of patrolling males.

seems a good explanation...

cause they want to annoy you and make it hard for you to kill them

I know this is not a great answer, but they don't always fly in circles for starters. I find the little pests usually fly to a place where they can have a meal.