As the past of will, for example in indirect speech
"The next meeting will be in a month's time" becomes
He said the next meeting would be in a month's time.
Polite requests and offers (a 'softer' form of will)
Would you like another cup of tea?
Would you give me a ring after lunch?
I'd like the roast duck, please.
In conditionals, to indicate 'distance from reality': imagined, unreal, impossible situations
If I ruled the world, every day would be the first day of Spring.
It would have been better if you'd word processed your assignment.
After 'wish', to show regret or irritation over someone (or something's) refusal or insistence on doing something (present or future)
I wish you wouldn't keep interrupting me.
I wish it would snow.
(This is a complicated area! Check in a good grammar book for full details!)
Talking about past habits (similiar meaning to used to)
When I was small, we would always visit relatives on Christmas Day.
Future in the past
The assassination would become one of the key events of the century.