There are some you can clean out. From the
Linux Documentation Project page for /var:
/var/cache
Is intended for cached data from applications. Such data is locally generated as a result of time-consuming I/O or calculation. This data can generally be regenerated or be restored. Unlike /var/spool, files here can be deleted without data loss. This data remains valid between invocations of the application and rebooting of the system. The existence of a separate directory for cached data allows system administrators to set different disk and backup policies from other directories in /var.
/var/log
Log files from the system and various programs/services, especially login (/var/log/wtmp, which logs all logins and logouts into the system) and syslog (/var/log/messages, where all kernel and system program message are usually stored). Files in /var/log can often grow indefinitely, and may require cleaning at regular intervals. Something that is now normally managed via log rotation utilities such as 'logrotate'. This utility also allows for the automatic rotation compression, removal and mailing of log files. Logrotate can be set to handle a log file daily, weekly, monthly or when the log file gets to a certain size. Normally, logrotate runs as a daily cron job. This is a good place to start troubleshooting general technical problems.
(See the documentation for some specific files in /var/log directory.)
/var/mail
Contains user mailbox files. The mail files take the form /var/mail/'username' (Note that /var/mail may be a symbolic link to another directory). User mailbox files in this location are stored in the standard UNIX mailbox format. The reason for the location of this directory was to bring the FHS inline with nearly every UNIX implementation (it was previously located in /var/spool/mail). This change is important for inter-operability since a single /var/mail is often shared between multiple hosts and multiple UNIX implementations (despite NFS locking issues).