I came across this error today while at work. While trying to process a MySQL dump of a database of approximately 8 GB in size, I got the following error:
mysqldump: Got error: 2008: MySQL client run out of memory when retrieving data from server
This occurred on a MySQL 4.1 server. To get around this, you will need to use the -q switch as part of your mysqldump command.

This option is useful for dumping large tables. It forces mysqldump to retrieve rows for a table from the server a row at a time rather than retrieving the entire row set and buffering it in memory before writing it out.

(source: MySQL :: MySQL 3.23, 4.0, 4.1 Reference Manual :: 4.5.4 mysqldump — A Database Backup Program)

Your full command should look something like this:
$ mysqldump -u user -p password -q database > outfile.sql