Arabic
Tai or al-Ta'i, at-Ta'i (الطائي), also spelled al-Ta'i or at-Ta'iy, is an Arabic name. In ancient times it originated as a nisba indicating affiliation with the Tayy tribe.
Chinese
Tái is the Pinyin romanisation of the Chinese surname written using the character 邰. According to traditional stories recorded in the Shuowen Jiezi, it originated as a toponymic surname referring to the city by the same name.
Tai may also be the Wade-Giles transcription of Dai (戴); see that page for people with that Chinese surname.
Japanese
As a Japanese surname, Tai could be written with the single characters 太, 台, 泰, or 載, as well as numerous two-character combinations from one character read ta (e.g. 田, 多) and another read i (e.g. on-yomi of 衣 or kun-yomi of 居 or 井). People with these surnames include:
Korean
Tai is an alternative spelling of the Korean surname Tae (太, 태). In a study by the National Institute of the Korean Language based on 2007 application data for South Korean passports, it was found that 28.5% of people with that surname spelled it in Latin letters as Tai in their passports, vs. 57.1% as Tae.