Try this revised query:

Declare @xml xml

Set @xml =

'<XML>

<Provider>

<providerID>1</providerID>

<Address>address1</Address>

</Provider>

<Provider>

<providerID>2</providerID>

<Address>address2</Address>

</Provider>

<Provider>

<providerID>3</providerID>

<Address>address3</Address>

<city>kol</city>

</Provider>

</XML>'

SELECT t.c.value('providerID[1]', 'int') AS 'ProviderID'

, t.c.value('Address[1]', 'varchar(100)') AS 'Address'

, t.c.value('city[1]', 'varchar(100)') AS 'City'

FROM @xml.nodes('/XML/Provider') AS T(C)

This outputs it in the format that you have specified.