"Guò Nián Hǎo (过年好)" or "Xīn Nián Kuài Lè (新年快乐)" ... The Chinese New Year is often accompanied by loud, enthusiastic greetings, often referred to as 吉祥話 (Jíxiánghùa), or loosely translated as auspicious words or phrases.  Some of the most common examples may include:

Happy New Year
Traditional Chinese: 新年快樂; Simplified Chinese: 新年快乐; pinyin: Xīnnián kuàilè.  A more contemporary greeting reflective of western influences, it literally translates from the greeting "Happy New Year" more common in the west.

Congratulations and be Prosperous
Traditional Chinese: 恭喜發財; Simplified Chinese: 恭喜发财; pinyin: Gōngxǐ fācái; Cantonese: Kung hei fat choi (also spelt kung hei fat choy or kung hey fat choi), which loosely translates to "Congratulations and be prosperous".  Often mistakenly assumed to be synonymous with "Happy new year", its usage dates back several centuries.  While the first two words of this phrase had a much longer historical significance (legend has it that the congratulatory messages were traded for surviving the ravaging beast of Nian, although in practical terms in may also involve surviving the harsh winter conditions), the last two words were added later as capitalism and consumerism ideas took greater significance in Chinese societies around the world.

The saying is now commonly heard in English speaking communities for greetings during Chinese New Year in parts of the world where there is a sizable Chinese-speaking community such as San Francisco's China Town.  In other English-speaking communities with a larger Chinese-speaking populations, the Mandarin versions tend to prevail especially when multiple dialect groups exist, particularly in Malaysia and Singapore.

Other Greetings
Numerous other greetings exist, some of which may be exclaimed out loud to no one in particular in specific situations.  For example, as breaking objects during the new year is considered inauspicious, one may then say 歲歲平安 (Suìsuì píng'ān) immediately, which means everlasting peace year after year. 歲 (Suì, meaning "age") is homophonous with 碎 (meaning "shatter"), in demonstration of the Chinese love for wordplay in auspicious phrases. Similarly, 年年有餘 (Niánnián yǒuyú), a wish for surpluses and bountiful harvests every year, plays on the word yú to also refer to 魚 (meaning fish), making it a catch phrase for fish-based Chinese new year dishes and for paintings or graphics of fish that are hung on walls or presented as gifts.

Other circumstances which may trigger the use of these greetings or phrases may be when children greet their elders just before receiving their red packets, when gifts are exchanged, during visits to the temples, or even when tossing the shredded ingredients of Yusheng - particularly popular in Malaysia and Singapore.