Even if you can speak no other words of Thai, most European and American visitors to Thailand will quickly become familiar with the Thai word farang (often mispronounced (even by Thais) as falang - farang with a slightly trilled 'r' is the correct pronunciation.) It's basically used to describe caucasians, though African-Americans will sometimes also be known as farang or as farang dam ('black farang'). Farang is also the Thai word for the guava fruit, so you can expect to hear farang eating farang 'jokes' if you happen to purchase any.
Other Asians are generally known by their country of origin (e.g. kon jeen - "Chinese people", kon yee-bpun - "Japanese people"), while people from the Indian Subcontinent are often known as kairk (which translates as "guest"). Kairk is used to describe even fluent Thai speakers of Indian descent who have been living in Thailand for generations and consider themselves as Thai - obviously being referred to as a 'guest' in these circumstances, while not particularly offensive, is not exactly complimentary either.
Some people get very offended at being called farang, but whether it's an insult should or not really depends on the context. A few Thais who are uncomfortable with using it will say kon dtahng bpra-tayt ('people from other countries') instead, but this is still pretty rare. Farang is basically a neutral word, but people who respect you (or who should respect you) will not use it - if you hear a work colleague, for example, refer to you as farang they probably mean it as an insult while a taxi driver or market vendor doing the same is unlikely to mean any offense at all.