If you don't need to do math on it (i.e., it's a credit card number),
preformat the cell as Text or prepend an apostrophe (').

If you need more than 15 decimal digits of numerical precision, you'll
either need to use a different application, or load one of the add-ins
that claim to extend precision to 200 digits (do a Google search, there
are at least 2).

You'll have to format the cells for text.  Format - Cells - Number - Text.
Then type the numbers.  Or precede each with an apostrophe (').

Hi
if you really need to calculate with theses numbers (e.g. they are not
credit card or telephone numbers) see for one add-in:
http://www.big-numbers.com/

Note: haven't tested this add-in by myself