A good conscience is a soft pillow

You sleep well when you have nothing to feel guilty about.

A good beginning makes a good end

If a task is carefully planned, there's a better chance that it will be done well.

A friend to all is a friend to none

Someone who is a friend to everyone makes none of them feel special.

A friend in need is a friend indeed

Someone who helps you when you are in trouble.

A fool and his money are soon (easily) parted

A foolish person usually spends money carelessly.

A chain is no stronger than its weakest link

The strength of a group depends on each individual member.

A burnt child dreads the fire

A bad experience will make people stay away from certain things.

The apple doesn't fall far from the tree

Definitions:
CD: a child usually has a similar character or similar qualities to his or her parents
UD: refers to a father/mother and son/daughter not being different from one another or being identical in their actions, behaviors, etc.  -
WT: A child grows up to be similar to its parents, both in behavior and in physical characteristics.

Examples:
Her daughter soon showed her own musical talent, proving that the apple doesn't fall far from the tree.
Dad gets caught stealing in his teen years and then his son gets caught stealing as a teen.

A bird in hand is worth two in a bush

It's better to keep what you have than to risk losing it by searching for something better.

An idle brain is the devil's workshop

When you work you avoid temptation.

An apple a day keeps the doctor away

A small preventive treatment wards off serious problems.

All work and no play makes Jack a dull boy

Everybody needs a certain amount of relaxation. It is not good to work all the time.

All's well that ends well

There is a solution to everything even though there are doubts.

All is fair in love and war

Things that are done in love or war can often be excused.

All that glitters is not gold

Appearances can be deceptive.