SQL Call Stored Procedure for each Row without using a cursor

Generally speaking I always look for a set based approach (sometimes at the expense of changing the schema).

However, this snippet does have its place..

-- Declare & init (2008 syntax)
DECLARE @CustomerID INT = 0

-- Iterate over all customers
WHILE (1 = 1) 
BEGIN  

  -- Get next customerId
  SELECT TOP 1 @CustomerID = CustomerID
  FROM Sales.Customer
  WHERE CustomerID > @CustomerId 
  ORDER BY CustomerID

  -- Exit loop if no more customers
  IF @@ROWCOUNT = 0 BREAK;

  -- call your sproc
  EXEC dbo.YOURSPROC @CustomerId

END

You could do something like this: order your table by e.g. CustomerID (using the AdventureWorks Sales.Customer sample table), and iterate over those customers using a WHILE loop:

-- define the last customer ID handled
DECLARE @LastCustomerID INT
SET @LastCustomerID = 0

-- define the customer ID to be handled now
DECLARE @CustomerIDToHandle INT

-- select the next customer to handle    
SELECT TOP 1 @CustomerIDToHandle = CustomerID
FROM Sales.Customer
WHERE CustomerID > @LastCustomerID
ORDER BY CustomerID

-- as long as we have customers......    
WHILE @CustomerIDToHandle IS NOT NULL
BEGIN
    -- call your sproc

    -- set the last customer handled to the one we just handled
    SET @LastCustomerID = @CustomerIDToHandle
    SET @CustomerIDToHandle = NULL

    -- select the next customer to handle    
    SELECT TOP 1 @CustomerIDToHandle = CustomerID
    FROM Sales.Customer
    WHERE CustomerID > @LastCustomerID
    ORDER BY CustomerID
END

That should work with any table as long as you can define some kind of an ORDER BY on some column.

DECLARE @SQL varchar(max)=''

-- MyTable has fields fld1 & fld2

Select @SQL = @SQL + 'exec myproc ' + convert(varchar(10),fld1) + ',' 
                   + convert(varchar(10),fld2) + ';'
From MyTable

EXEC (@SQL)

Ok, so I would never put such code into production, but it does satisfy your requirements.