In Western culture there are numbers that might be considered auspicious or inauspicious such as the unlucky #13 or lucky #7. In Chinese culture they have there own sets of numbers which is useful to understand especially to avoid a situation where you might unintentionally offend someone.
There is a Chinese saying: "good things come in pairs". So this number is considered auspicious especially for marriage, you'll often see 雙喜 (shuāngxǐ) at weddings which translates to double happiness .
The number 4 in Mandarin sounds like 死 (sǐ) which means Death, because of this association this number is considered a inauspicious number. In many asian countries you'll find that number 4 get's omitted from many things including elevators or telephone numbers and more importantly hospitals.
So if you do find yourself in a hospital don't freak out when you can't find the forth floor or room, you're not losing your mind. In fact it's so common in Asia, it even has a name Tetraphobia.
Number 7 is one of those numbers that could be considered auspicious or inauspicious. It is considered lucky for relationships with it sounding similar to Mandarin words like 齊 (qí; even) or 氣 (qì; life essence).
However during July it can be considered inauspicious as it coincides with 鬼節 (guǐjié; Ghost festival)
The auspicious number 8 (八 bā) sounds like 發 (fā) which is the verb for 發財 (fācái; to get rich).
It's such an auspicious number that many people will go out there way to obtain the number such as having license plate with 88888, but if you follow the link prehaps it wasn't quite a lucky as first thought.
The number 9 (九; jiǔ) which sounds like the Chinese word 久 (jiǔ) which means long lasting. It is because of this it is often used for weddings.
520（五二零； wǔ èr líng）in Mandarin sounds similar to 我愛你 (wǒ ài nǐ) or I love you in English. As a gesture of love couples might send money to eachother in figures of 520.
514 (五一四； wǔ yī sì) in Mandarin sounds like 我要死 (wǒ yào sǐ) which means I want to die.
88 (八八； bābā) sounds similar to bye-bye.
748 (七四八; qīsìbā) which sounds similar to 去死吧 (qùsǐba) which means go to hell.
250 (二百五; èrbǎiwǔ) means stupid or half-insane.