1. Congratulations!

You can say Congratulations in many circumstances, such as for weddings, promotions, passing exams, or to the parents and family of a new baby.

2. Well done!

You can say this to someone who has passed an exam or achieved something difficult like a promotion.

3. Birthdays

The most usual ways of referring to someone's birthday are by saying Happy Birthday! or more formally, Many more to come!

Cultural note: Some birthdays are more special than others in some countries. Your 18th birthday is special as you then become an official adult. In the past, 21 was the age of adulthood, and some people still celebrate it in a special way by giving silver keys, which represent the key to the door.

4. Before an exam or something difficult

Wish someone good luck before something difficult, by saying Good luck! But if people are superstitious and believe that saying "Good luck" will have the opposite effect, you could also hear Break a leg!

5. Toasting

At parties and gatherings, you might be asked to drink a toast to celebrate a happy event. Here's to …

Let's drink to…

Ladies and Gentlemen, "The Bride and Groom". Please raise your glasses to (state the name).

6. Writing wedding cards

Here are a couple of standard phrases to write on wedding cards:
Congratulations! Wishing you many happy years together.

Wishing you the best of luck in your future together.

7. Writing in sad situations

In difficult situations you can write I was so sorry to hear that ….

If you are writing to the relatives of someone who has died, you can also write:
I was deeply saddened to hear…
or
Please accept my deepest condolences on the death of…
(You can replace "I" with "We", such as "We were very sad to hear that…")