It’s uncommon that travelers come across dangerous/poisonous animals, but it also depends on where you go. In Bangkok, you’ll not encounter many dangerous animals, while you should be more careful when going to rural areas, the jungles, or to the islands.
To summarize, you should primarily look out for the following animals: snakes, centipedes, scorpions, and jellyfishes. Snakes can turn up everywhere, sometimes even in the cities. Be sure to get medical treatment as early as possible if you get bitten by any of these animals.