I have to have an important document sent to me from the USA to Bangkok. I would like to use FedEx or UPS, but I may not be home to sign for it. Does anyone know the the most secure way to send it, without requiring a signature? Would it be USPS priority mail?

With FedEx you can have it sent designating for hold at the specific FedEx office nearest to you for pick up.

I would suggest using the good ole USPS, registered. Might even have it sent "return receipt". Such mail is brought to my door and the mail lady rings the bell for a signature. When no one is home to sign, she leaves a notice and I go pick it up and sign for it.

Have the sender send you the tracking number and you can track it from home.

I usually take one of the two below possibilities:

With FedEx, DHL, UPS the sender can give the instruction to call and arrange for a delivery appointment. Then you can arrange the delivery to a place of your convenience. This has worked quite well for me in the past.

In my condo all registered items are signed for by the management office. They will leave a card in my mailbox and I have to counter sign once I pick up the package. Maybe it is the same at our place?

This is a list of FedEx Service locations in Bangkok and elsewhere in Thailand. If it really is an "Important Document" I would not let it go out for delivery by anyone with maybe some third party signing for it or having to make appointments for delivery..

There are enough FedEx locations with most open Saturdays

http://www.fedex.com/th/dropoff/

I use FedEx from the US and DHL from the UK. Although I am named as recipient, for both delivery addresses I list their respective main offices in Pattaya but the contact phone number I list is mine. That way there's never an issue of missing a delivery to the house when I am out. I particularly like DHL as they call me when they have received it. I just collect it with my photo ID (Thai DL) and a signature.