Everyone has to pay it, companies as well, but a VAT registered company can claim the VAT back - there's a famous (and true) example of it!.
A lumberjack company chops down trees, and sells to a sawmill, the sawmill pays VAT to the lumberjacks, who pass it on to the VAT office. The sawmill then claims the VAT back.
The sawmill saws the wood and sells it to a pulp mill - VAT is paid and claimed back again.
The pulpmill sells the pulp to a paper factory - again VAT is charged and claimed back.
The paper factory makes the pulp into paper, and sells it to a bag manufacturer - VAT is paid and reclaimed.
The bag manufacturer makes it into paper bags, and sells them to shops - VAT is paid and claimed back by the shop keeper.
The shop keeper then gives the paper bag away, with apples or something inside it, as it's given away there's no VAT.
So all that money has gone back and forth, and it ends with not a penny been paid in VAT