Basically it concerns Virtual Dedicated Server (VDS / VPS), because has default installation of MySQL on CeontOS / Fedora / RHEL to default my.cnf does malloc a hundred-odd megabytes.
Of course the memory consumption of MySQL influence such parameters as key_buffer, query_cache_size etc. But they by default are minimal, and the cache queries at all on my disabled by default.
So that's all very simple. Add to my.cnf:
skip-innodb skip-bdb
Handler is disable InnoDB, BerkeleyDB and the entire consumption of memory. Well of course it should be done if you do not use the above types of tables.
Next restart MySQL and in top see that it takes a dozen or two megabytes.
In most cases will not prevent option and skip-networking. But thread_cache_size I advise to put a value of 5-15 (depending on load)