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Mandarin Chinese is romanised as pinyin.
黥 Branding Criminals
Qíng (黥) means 'to tattoo' in Chinese: In feudal China, tattooing was a form of punishment; criminals had their crimes tattooed on their faces for all to see. Qíng miàn qiú tú (黥面囚徒) is the expression for a branded criminal.
The story is told of the Song Dynasty General, Yuè Fēi (岳飛). While serving in the Song army, fighting the invading Jurchens, the Field Marshal he served under defected to the enemy. In disgust, he left the army and returned to his home town to look after his aging mother. Upon his return, his mother did not welcome him, but instead admonished him, saying that his first duty was to his country and not to her. To remind him of this, she tattooed this phrase on his back: 盡忠報國 'The greatest loyalty is to serve one's country'.
天地會 Triads
Tatoos have been proudly worn by members of the triads since Qing Dynasty times. The tattoos are often elaborate, covering much of the body, and feature Chinese characters mixed with mythical animals such as dragons and phoenixes.
There are probably two reasons for the use of tattoos by the triads. The first reflects their origins as organised resistance against the Manchu conquerors. Branded criminals were probably proud of their status as people marked as being outside the Manchu establishment.
The second reason is probably that in modern times, joining a triad usually means forsaking your own family and taking them as your new family. The tattoos would therefore mark you as belonging to a particular triad gang; but also, because of the aversion mainstream Chinese society has to tattoos, mark you as something separate from society.
刺靑 Modern Chinese tattoos
Cì qīng (刺靑) is the modern Chinese expression for tattoos. It is a purely descriptive term, meaning 'pricking black', and does not carry the same negative connotations that 黥 does. There is even a more poetic expression, wén shēn (紋身), that literally means 'body patterns' and actually sounds quite nice.
預告 Caveat
Requests for Chinese phrases or translations for tattoos will meet with a frown from most Chinese. It is simply not the "done thing". Tattoos are seen to defile and not to beautify the body; Chinese brought up in Western societies often have a more open-minded attitude to it, but will often not know enough Chinese to give proper advice about suitable phrases! See http://hanzismatter.com/ for examples of disasters (thanks BlackPawn).