What is the Issue Number?
The Issue Number on a card was put in place in order to enable a static card number to be changed in the event of a re-issue requirement, such as a loss or theft.
The Card number would be made up of a fixed prefix, to identity the card type, and the sort code and account number associated with the card. The problem with this was that if the card needed to be reissued, the number on the front could not be changed without creating an entire new account underneath it. Hence, the Issue Number was introduced to enable the card to be differentiated from a previous issue of the same card number.
This was particularly prevalent in the UK when Switch was an extremely common method of Debit Card payment.
Its use today
Switch/Maestro/Solo
Switch was merged with Maestro, the international debit card brand of MasterCard, in 2002. As such, no valid Switch Cards are in existence today.
In 2011, MasterCard merged the UK Domestic Maestro with the standard international, ending its status as a separate card scheme. This also led to the discontinuation of the Solo card scheme too.
Therefore until 2011, cards were being issued where Issue Number could theoretically be required. However, any card issued then should now have expired and, as such, any valid card today in this card scheme should not require an Issue Number.
American Express
Contrary to some belief, American Express cards do not have an issue number [1]. They do have a two-digit reference on the front but this refers to the 'Member Since' year and is often confused with an Issue Number. It is not required by online merchants accepting American Express.
AMEX does differ from most cards, but in the Security Digits that appear on the back of most cards. AMEX has four digits, instead of the usual three, and prints these on the front of the card.
[1] http://blog.unibulmerchantservices.com/10-signs-of-a-valid-american-express-card/