What algorithm to use to calculate a check digit?

The Luhn algorithm is good enough for the credit card industry...

As RichieHindle points out, the Luhn algorithm is pretty good. It will detect (but not correct) any one error or transposition (except a transposition of 0 and 9).

You could also consider the algorithm for ISBN check digits, although for old-style ISBN, the check digit is sometimes "X", which may be a problem for you if you're using integer fields. New-style ISBN doesn't seem to have that problem. Wikipedia doesn't go in to the theoretical properties of the system, but I remember studying ISBN numbers in my coding theory course long ago, so I think they are pretty good :-)

I know it is a bit late (according to post dates), but first time I needed a check number algorithm was last week.

So I checked more algorithms and IMHO the best solution seems to be the Damm algorithm. It is simple to implementation and detect most of tested errors. With default digit check table all single digit errors, all English language mishearing errors, all adjacent transposition errors, and almost all jump transpositions errors are detectable.

For me there was only a single problem, since I need to calculate check digit not only from numbers but also from characters. Unfortunately for me, there was a given rule, that the last character must be a digit; or better to say, the characters were assigned by third party authority and only fixed amount of numbers were used as manufacturer number.

There are many ways how to transcribe characters to number, but the error detection will always be lower, comparing to when only numbers are used.

For these cases you can use the ISO_6346 specification.

When there is no such limitation, use the tables for different size and assign characters and number to table values.

EDIT: updated/fixed description, added reason for digit check number for characters, and added tables for different base sizes.