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In my Rails 3 app, I am creating a Book model which contains an ISBN column. This ISBN value will be a number 13 characters long. Which type should I use to create the ISBN column? Should I use an :integer or a :string? What is the maximum size of an integer in Rails?

rails g scaffold Book title:string isbn:integer
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The maximum size of the integer depends on the database being used. For MySQL it's 2147483648 (2^31 since it's an unsigned integer.) I would recommend you store the ISBN as a string (likely a CHAR(13) if possible.)

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not convinced by that reasoning. one can use a 64 bit integer too (10^19). books are not going to grow so fast as ISBN itself has a 10^13 search space.
True. If I was answering this today I would recommend a BIGINT (rails :integer, limit: 8 to force a BIGINT.)
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ISBN numbers also contain characters i.e hyphen(-) which obviously you cannot store in integer form. So I would recommend you to use string.

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ISBN things like thisISBN 978-7-111-27687-6,so obviously string is a good choice

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I think a good rule of thumb is using numerical fields when you need to do math operations on the fields (or when there is a chance you would do it at some point). If not, it is a very good candidate of being an string.

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I am not sure if that should be a thumb rule. if the search space is going to be small enough and not going to exceed the max number limits in future, integer makes a very good datatype as its fast on comparison.

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