Does a read-only MySQL slave need log-bin in addition to relay-bin logs?
You are right. Traditionally, replication slaves need binary logs enabled unless you plan to failover to it someday.

The only reasons for using binary logs on a slave would be


Setting you circular replication (Makes a Slave a Master at the same time)
You want to promote the Slave to a Master
Using it as a Distribution Master (All Binary Logs,No Data, See my old post Is it Possible to Recover Data from a BLACKHOLE table? that describes why one would use such a setup)


As for your actual situation, here are two suggestions (pick one)

SUGGESTION #1

First, login to mysql as root@localhost on that slave and run 

mysql&gt; STOP SLAVE;
mysql&gt; RESET MASTER;


Next, comment out this line from my.cnf

#log_bin                         = /var/log/mysql/mysql-bin.log
#log_slave_updates               = 1


Next, restart mysql

service mysql restart


Finally, manually delete those logs

cd /var/log/mysql
rm -f mysql-bin.*


SUGGESTION #2

If you do not want to restart mysql, do this

First, login to mysql as `root@localhost on that slave and run 

mysql&gt; SET GLOBAL expire_logs_days = 1;
mysql&gt; RESET MASTER;


Then, add this line to my.cnf

expire_logs_days = 1


That way, the slave would still pile up binary logs, but would auto delete binary logs older than 24 hours.

GIVE IT A TRY !!!