Thailand is not as cheap as it used to be with Bangkok recently being named the second most expensive city in south east Asia behind Singapore. However, budget travelers who are careful with what they spend will still find 1,000 baht will get a backpacker a dorm bed or cheap room, three square meals a day and leave enough for transport, sightseeing, and even partying (edit: as of March 2019 this is very difficult to achieve). Doubling that budget will let you stay in decent 2-star hotels, and if you're willing to fork out 5000 baht per day or more you can live like a king. Bangkok requires a more generous budget than upcountry destinations, but also offers by far the most competitive prices for shoppers who shop around. The most popular tourism islands such as Phuket and Ko Samui tend to have higher prices in general. It is common for tourists to be charged several times the actual price in tourist areas of other places, as well. If you do want to have an idea what the real Thai prices are - consider visiting local markets, as well as malls like Big C, Tesco or Carrefour where locals and expats do routinely shop. Those are available in any major cities (in Bangkok, there are dozens of them) and even on some larger islands such as Phuket or Ko Samui.
Any travellers on a tight budget would be well-advised to avoid all of the touristy destinations entirely, and head to the North-Eastern region of the country known as Isaan, which, although much quieter and subdued, offers a more authentic taste of the country
with all the tourist-traps and scams which can be found in the capital and island destinations.
The Thai baht seems to be strengthening, and combined with crippling inflation, things are no longer that cheap any more. If you want to stay in luxury, and eat in the best restaurants and enjoy the nightlife, you can easily burn through $500 (or more) a day!