One approach:
1) Edit>GoTo. Click "Special". Select "Visible Cells Only". Click OK
2) Copy the selection you just generated
3) Paste it onto a new, empty sheet (or PasteSpecial>Values if appropriate)
This will give you a new sheet with everything that was visible (and only
that which was visible) on the old sheet. You can then delete the old sheet
if desired (and if formulas haven't been broken).
Note that this method can be applied to filtered lists, outlines, etc. as
well.
Hope this helps,