Can I print to a different notebook? (within the context of the same kernel)

As Yves already mentioned, you can easily create and edit notebooks through Mathematica commands. A start would be this tutorial, which you can find in the Documentation Center under tutorial/ManipulatingNotebooksFromTheKernel

Here is a short example printing the i values into a new notebook:

nb = CreateDocument[];

For[i = 1, i <= 10, i++,
 SelectionMove[nb, Next, Cell];
 NotebookWrite[nb, 
  Cell[BoxData@RowBox[{"i is now ", ToString[i]}], "Output"]];
]

If you want to know how to construct cell expressions, you could just go over any cell in a notebook and hit Ctrl+Shift+E to see the underlying structure.

Although the question has been answered, no reason for this question was given. One possible motivation is to be able to discard a lot of diagnostic output, e.g. from an iterative process, by trashing the newly created notebook.

In such a case an alternative could be Dynamic[.], e.g.

ClearAll[iter];
Dynamic[iter]
For[i = 1, i <= 10, i++,
    Pause[1.0];
    iter = "i is now " <> ToString[i]
]

Here's what I have been using.

Any improvements / comments are welcome.

(* this opens a notebook file and if notebook exists it CLEARS the contents as well  *)
OpenNB[fname_] := Module[{dir, fns, nb},
   dir = NotebookDirectory[];
   fns = FileNames[FileNameJoin[{dir, fname}]];
   If[fns === {}, (
     nb = CreateNotebook[];
     NotebookSave[nb, FileNameJoin[{dir, fname}]];
     ), (
     nb = NotebookOpen[fns[[1]]];
     SelectionMove[nb, All, Notebook];
     NotebookDelete[nb];
     )
    ];
   Return[nb];
   ];

PrintNB[style_String: "Print", nb_NotebookObject: EvaluationNotebook[], args__] := NotebookWrite[nb, Cell[BoxData@ToBoxes[SequenceForm[args]], style]];

Here is example usage

logNB = OpenNB["log.nb"];
PrintNB[logNB, "Execution Log for: ", NotebookFileName[]];
PrintNB[logNB, "Started at: ", DateString[]];

f[r] = r^\[Gamma]*Exp[-\[Kappa] r];
PrintNB[logNB, "f(r) = ", f[r]]; 
PrintNB["PageBreak", logNB, " "];
PrintNB[logNB, "Hello"];

Here is the output