Health care in Thailand is generally easily accessible, inexpensive and of high quality, so if you do end up needing to see a doctor or visit a hospital while you're on vacation in the Kingdom, you don't need to worry.
Bangkok has numerous private international hospitals catering to locals, expats and tourists. The three most popular are Bumrungrad, BNH and Samitvej. All have multilingual nursing and support staff. Doctors at these hospitals are all fluent in English and often another language in addition to Thai, plus many have been schooled and/or trained at top medical schools all over the world.
Phuket, Pattaya, Chiang Mai, and Samui also have large international hospitals that specifically market and cater to foreign travelers and residents. Although they often don't have the breadth of specialists you'll find in the capital, they have sufficient facilities and doctors to treat nearly any common illness or injury.
The cost to visit one of these hospitals is surprisingly affordable (especially considering that the nicest ones in Bangkok resemble five star hotels). For a basic office visit, expect to pay around $20 excluding the cost of any special tests, medications or procedures. If you have to visit the emergency room, the visit itself will typically be under $100, again excluding additional costs. Bumrungrad's website provides cost estimates for common procedures to give you a sense of prices.
Outside of the country's high end private hospitals health care is much less expensive and there are good hospitals and excellent doctors even at the public level, though you will run into a language barrier in most.
Common Illnesses. Be aware of the types of illnesses travelers to Thailand are likely to get and what you can do to protect yourself against them. Traveler's diarrhea is the most common ailment tourists to the Kingdom suffer from, but heat exhaustion, severe sunburns, jelly fish stings and motorcycle-related injuries are also very common.
Vaccinations. For the most part, vaccinations are not required before visiting Thailand, but there are some precautions you should take. Learn more about the US Government's Travelers' Health Warning System
Mosquito-borne Illnesses. One thing many people (some doctors included) mistakenly believe is a threat in Thailand is malaria. Malaria is rarely seen in most parts of Thailand, including Bangkok, the islands and the Chiang Mai area. It can be a problem in the deep jungle near the borders but tourists rarely visit that part of the country anyway. Anti-malarial drugs are serious and can have significant unpleasant side effects. Talk to your doctor but in general avoid taking them unless you will be in regions where malaria is known to be present. That doesn't mean that you shouldn't worry about mosquitoes, as Dengue Fever is a serious disease transmitted by mosquitoes that people in built-up urban areas, including Bangkok, are susceptible to. Make sure to protect yourself against mosquitoes, especially during rainy season
Pharmacies and Prescription Drugs. Pharmacies in Thailand are allowed to dispense many medications that can only be obtained by prescription in the United States, including antibiotics, anti-malarial medication and other drugs such as Cialis and Viagra. Note that pharmacies are not allowed to dispense opiate pain killers or mood-altering drugs. If you will need to have a prescription refilled while in Thailand, make sure you have a doctor's note and know the generic name of the drug as well. Some medications are not available in Thailand or are sold under a different name. In any case, for some drugs, you may need to visit a hospital and be seen by a doctor before you can get your prescription refilled.
Medical Insurance. Check your medical insurance plan to see if you are covered for emergencies overseas, and, if so, to what extent before investing in additional insurance. Most plans cover at least emergency care, even if the deductible is high, but don't cover extreme measures such as med-evacs back to your home country. Read more about travel insurance.