It should be worn in the non-dominant wrist. Normally dominant hand is used for writing, eating and many other day-to-day activities those may likely to exaggerate activities of the subject.  

Thank you Atanu. I agree with this also. 

Agree with Atanu Pati.

Also the very most of the scientific actigraphy literature used this standard (e.g. non-dominant wrist).

Agree with Atanu. This was the protocol used for the feasibility respiratory muscle training study done with healthy snorers in my MA Res Sc. 

Thank you very much Pierre and Marianna. 

most of popular devices (fitbit, withings, polar, ...) are actually unuseable for scientific research. Perhaps with reverse engeneering to understand their communication protocol we can use them.

I thought that wearing it on the dominant wrist would be better able to distinguish quiet sitting, like in front of TV, from sleeping.  But when I tried to wear it on the dominant wrist I found it very annoying.  So that was the end of that!

I do agree with Atanu Pati. In most of the scientific literature on actigraphy, it is recommended to wear the actigraphy watches on non-dominant hand.

Thank you everyone for your comments. 

Left wrist for right handed and right wrist for left handed as it affect the working hand.

I agree with Dr. Mageet the activity level of the hand in question can affect the results.

It might be correct to use the non-dominant arm, but two references did not find any important differences:

Littner M, Hirshkowitz M, Kramer M, Kapen S, Anderson WM, et al. (2003) Practice parameters for using polysomnography to evaluate insomnia: an update. Sleep 26: 754–760.

Van Hilten JJ, Middelkoop HA, Kuiper SI, Kramer CG, Roos RA (1993) Where to record motor activity: an evaluation of commonly used sites of placement for activity monitors. Electroencephalogr Clin Neurophysiol 89: 359–362. doi: 10.1016/0168-5597(93)90076-2

I agree with Gunnar Morken. In the tests I have performed I found no differences between dominant and non-dominant arm. 

However, I would recommend following the recommandations of AASM (see : Ancoli-Israel S. 2003 SLEEP, the section on actigraph placement).