Tipping is not common in Thailand and the Thais themselves don't do it. Thais do round up (or down) the taxi fare to get it to an amount that is easier to pay for (such as from 59 or 61 to 60 baht). Sometimes they also leave the change in restaurants, but even this is a rare occurrence.
You don't have to feel odd if you don't tip at all, as that's what the locals do, but the presence of many foreign visitors have changed some expectations. Tipping is now common in many high-end hotels and tourist restaurants. Don't go overboard when tipping — never give more than 50 baht. In some tourist places, especially along Khao San Road, there are even restaurants hinting for a tip. This is not common (and even rude) in Thai culture, so you can easily ignore it.
Do not tip when a customer service charge is applied, as this is supposed to be the tip, applied only in luxury restaurants and hotels.