Most taxis have seatbelts however there are those which do not. It is possible to hire a taxi with a car seat for babies in larger cities however make sure you book these in advance. Bringing a car seat with you to Thailand can be cumbersome particularly if you plan on moving around however, most airlines will offer two carry 2 pieces of baby equipment free of charge. If you are bringing your stroller, your car seat could be your second piece of equipment. For further information on travel safety click here.
Tuk tuks are a popular form of transport in Bangkok. These are essentially motorbikes with seating hitched to the back or built around the bike. These are definately not the safest way to travel as they are open and generally do not have safety belts.
If you are staying in Bangkok a great option is to book a hotel on the river. Many of the more expensive hotels have a boat running between them. This is a safe and convenient way to travel and many of Bangkok’s most famous sites will be inclose proximity to the stops.