Depends on where you live. In Queensland, Australia, If it's registered, the dealer should take care of everything, you'll get a copy of the safety cert, your receipt and a copy of the rego transfers. If it's private you need a receipt, if it's rego'd you will need transfer papers and a copy of the last reg slip.

Get a receipt from the seller, that's all you need for a bicycle, at least here in the UK.

I took the liberty of placing your question in the correct category which is ALL>Cars & Transportation>Motorcycles.

In the future, check the Suggested Category and if necessary change it before submitting.

nothing, just buy the bike and sign a contract

if it is a motorcycle... then you will need to check it's current registration or if it is a stolen or not and if there is any finance on it or not. and of course a buyer seller agreement.

bicycle? just receipt

or nothing

take bike and go