If you need something formal 如果需要正式一點

1.  Allow me to introduce myself.  請容我介紹自己
2. Good morning/afternoon! 早安/午安
3. How are you? 你好嗎?
4. Hope this email finds you well. 我希望你收到此信時一切都好 / 收信好 / 收信安好 / 收信快樂 / 收信愉快
5. I hope you enjoyed your weekend. 希望你度過了一個美好的週末
6. I hope you're doing well. 希望你一切進行順利
7. I hope you're having a great week. 希望你有個很棒的一週
8. I hope you're having a wonderful day. 希望你有個美好的一天
9. It's great to hear from you. 很高興聽(收)到你的消息
10. I'm eager to get your advice on... 我非常希望得到你的建議
11. Thank you for reaching out us regarding... 感謝你主動聯絡我們 
12. Thank you for your help. 感謝你的幫助
13. Thank you for the update. 感謝你更新訊息
14. Thank you for getting in touch (with us regarding XXXX.)感謝你(就...事情)與我們聯繫
15. Thank you for the prompt reply. 感謝你的快速回覆
16. It has been awhile since we last spoke. 從上次談話至今也過了一陣子

If you're following up on something 如果要跟進事情

17. As promised, I'm... 如同之前承諾, 我...
18. As we discussed on our call... 同之前電話中所討論...
19. Can you provide me with an update on... 可以請你提供更新的...(資料)
20. I'm checking in on... 我正在核對...
21. I'm getting back to you about... 我要回覆你關於...
22. To follow up [our earlier decision] on meeting... 跟進我們[先前]在會議上[的決定]...

If you want to get (appropriately) personal 如果你想(適當地)私人一點

23. Congratulations on [recent accomplishment] 恭喜你[近期的成就/成績]
24. How did [recent project] turn out? [最近的案子]如何啊?
25. I hope you enjoyed your [event or vacation] 希望你享受你的[活動/假期]
26. I loved your recent [photo/article/social media post] 我喜歡你最近的[攝影/文章/網路po文]
27. I was just laughing the other day about [inside joke] 我前幾天笑過[內部梗]
28. I was just thinking about you and [shared memory] 我剛好想到你, 並[分享回憶]
29. It was great to see you at [event] 很高興在[活動]遇見你
30. This [article/video/GIF] made me think of you 這個[文章/影片/GIF]讓我想到你
31. [Mutual Contact] recommended I get in touch with you [共同認識的人]推薦我和你聯繫

If you're feeling funny 如果你想有趣

32. Happy "Not Monday" "非週一"快樂
33. Hello from the other side "
34. Here's the good news: Only [number] more days until Friday 有個好消息: 只要再過[數字]天就是星期五了
35. Hope you're surviving another workweek 希望你能從另一個工作日
36. I hope you've had your coffee already 我希望你已經喝過咖啡
37. It's me again 又是我~
38. I'll keep this short 我會長話短說
39. I'm sorry if this Message sabotaged "inbox zero" for you 我很抱歉這則訊息破壞了你信箱的"0封信件"
40. Just what you want: another email! 正是你想要的: 另一封郵件!