MySQL Partitions are a great way to rotate data in a table without incurring the overhead of running multiple delete statements. The most common use of this is to partition data by date. You must use MySQL 5.1 (or newer, I presume), and it is recommended to use MySQL 5.1.16 or later in order to take advantage of the ALTER TABLE features that allow adding partitions on existing tables.
This is an incredibly useful method of analyzing the queries that your MySQL server is processing without having to change the log level, and subsequently, not having to restart the MySQL server.
First, capture the MySQL queries with tcpdump as they come across the wire
tcpdump port 3306 -s 65535 -x -n -q -tttt > tcpdump.out
When you're done capturing the desired traffic, run mk-query-digest from Maatkit to analyze the tcpdump
mk-query-digest --type=tcpdump tcpdump.out | less
If your MySQL data lives on an LVM volume, using an LVM snapshot is a great low-impact method of getting a point-in-time backup of your entire database. The only real gotcha is that snapshot must be made while the data files are in a "safe" state (meaning that all of the data has been written to file, and not only present in memory). Here are the basic steps needed to get a backups
Purge Binary Logs
Purging binary logs can free up a lot of space in a crunch. These logs are primarily used for replication, and don't necessarily need to be kept for very long.