March 2013 Edit:
A very pertinent resource is the PCI Security Standards Council, an organisation founded in 2006 by five of the biggest global Credit Card brands (AmEx, Visa, MasterCard, JCB International and Discovery) and which is the de facto authority on Security matters for the Payment Card Industry (PCI).
This organization publishes in particular the PCI Data Security Standard, currently in its version 2.0 edition which covers issues such as the management of complete or partial credit card numbers. This document if freely available but requires a simple registration and acknowledgment of license terms.
The following is the original, c. 2009 answer, mostly correct but apocryphal.
A common practice (whether legal or not I do not know) is to store the last 4 digits, as this may be used to help the customer confirm which of his/her credit cards were used for a particular transaction.
Without significantly improving the odds of a malicious person guessing the complete number, one can store the first 4 digits which are representative of the financial institution which issued the card, as mentioned in the question.
Do NOT, save many more digits than these 8 digits because otherwise, given the LUHN-10 checksum, you may provide enough info to make guessing the complete number more plausible (if still relatively hard, even with insight from the series used by a given issuer, in a given time period, but one should be careful...)
To make this whole thing safer, technically and legally, you may consider only storing such info if the customer explicitly allows it. You should also consider masking this info with a simple hash for storing in the database.
Also, what you can / should store following a particular transaction, is the transaction ID supplied by the Credit Card Processor, at the time the transacton is submitted. This ID is the key that allows locating most (all?) of the info you would even need, would there be any issue with a particular transaction. This type of info can typically be queried from a secure web site maintained by the Processing company, along with some aggregate reports which may include a grouping by card-type (Amex, Visa...) if that is why you are thinking of storing the first four.