I play safe now, when I leave the village I make sure I carry my passport with me ... don't want to give the thieving bastards a chance to scam me.
I will only take mine if I am going out of province.
Just for info, this is the advice from Trip Adviser:-
Carrying Your Passport: It is required by Thai law that Thai citizens
AND all visitors
MUST carry proper identification at all times. This must be presented upon demand by a Police Officer or other legitimate Government Official.
NB: It is not always safe, practical or appropriate to carry your physical passport on you at all times. Passports are a very valuable commodity that can be the target of theft and are very expensive to replace while overseas. Consider keeping your passport locked in your room safe or the primary hotel safe at the reception desk while at each destination.
Do make several photocopies of your passports photo/details page, as well as the stamped arrivals card that is stapled in your passport that you received when entering Thailand. Carry these copies with you in your day-pack. These will assist in establishing your identity and immigration status when you don't have your physical passport on you.
Also consider making a colour scanned copy and having it laminated. If you produce that to an Official when required to, in many cases this will satisfy the identification requirement, or at least suffice until your actual passport can be collected from your accommodation for verification.