mysql binary log makes disk full
I guess one obvious improvement would be to use a different cache backend.

If you have a single server and enough memory, you could use an APC backend (D6: http://drupal.org/project/cacherouter, D7: http://drupal.org/project/apc) to have various of the often used caches directly in shared memory. That is probably the fastest cache solution you can get.

Another alternative is Memcached, which is especially interesting if you have multiples servers that should share a cache.

Note that you can't move the cache_form because that contains information about currently displayed forms and is not really a cache since it contains unique information, not just aggregated things like the others, which can always be cleared. Also, some other caches, especially cache_update, you might want to keep in the database, because that shouldn't be cleared like the rest as it contains information about update information of your used modules, something that doesn't change that often and can be very slow to re-fetch if you have many of them.

You can also move the sessions information out of the database, for example can you place it in MongoDB, and there are probably others too.