1. Affluent、well-off等是比较常用的表达：

Her family was very well-off.
她的家庭非常富有

I heard that she has a wealthy uncle.
我听说她有个非常有钱的叔叔。

He is becoming more and more affluent.
他越来越有钱了。

2. 也有不太礼貌的表达：

He ​inherited the ​family ​business - he must be loaded!
他继承了家族产业——肯定富得流油！

They're filthy rich.
这些人都太特么有钱了。

3. 近几年又兴起了一个说法——the one percent，“财富塔顶端的那1%”：

It's easy to get by in society when you're part of the one percent.
这个社会就是富人好办事儿。

4. 如果一个人从小就有钱，可以用privileged：

She had a privileged upbringing.
她是含着金汤匙长大的。

5. “新富”和“承袭祖荫”也各有说法：

These new money millionaires have been coming in and building these huge mansions in the area.
新晋的百万富翁们不断涌入，在那个地方建豪宅。

She comes from an old money family.
她家祖上就很有钱。