Borrowing

cover
つける

Can you cover dinner? I'll pay you back later.
飯はつけてくれる？後で返すし。

Comment:
This is used when going out with friends and you realize you have no money and need a friend to pay for you.

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tab
つけ

Put it on my tab.
つけにしておいてくれ。

Comment:
This is used when you need the store to cover you. The store might have a running total of how much money you have "put on your tab" which you would pay back later. I think this might be more common in small rural towns in the US - most normal people don't do this but you'll see it in movies a lot.

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owe
借りがある

I owe my friend $20.
友達に２０ドルの借りがある。

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I owe you one.
恩に着るよ。

Comment:
This is used when you are really thankful for something. It doesn't actually mean you will repay them anything, it's just an expression of thanks in normal usage.

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Neither a borrower nor a lender be.
借り手にも貸し手にもなるな。

Comment:
I think this phrase is pretty stupid. I don't think there's any problem with borrowing when you have to and forming debt that you repay since it helps form bonds.