Which tables are safe to clear?
Drupal 7 tables that can be excluded

Here is a list of tables in Drupal 7 that you can either clear (to reduce the database size) or safely exclude to do a migration (as in the question about How to reduce the locally exported database size to get around my server import limit?):


accesslog
batch
all cache related tables, such as:


cache*
cache_block
cache_content
cache_filter*
cache_form
cache_calendar_ical
cache_menu*
cache_page*
cache_views 
*_cache, such as features_cache or views_data_object_export_cache

ctools_views_cache
ctools_object_cache
devel_queries
devel_times
flood 
history 
queue
various search_* tables, such as:


search_dataset
search_index
search_keywords_log
search_total

semaphore
sessions
watchdog
webform_submitted_data


Usually tables such as search_index and watchdog use a lot of database space, so just eliminating those 2 tables can make a huge difference already.

Other tables that might be excluded

Check the size of your remaining tables and identify which one of them are the biggest in size.

Typically you might find session tables for which no cleanup procedure is in place. Such tables you can probably also exclude.

Module Backup and Migrate

To further reduce the challenge as detailed in "How to reduce the locally exported database size to get around my server import limit?", look at the Backup and Migrate module also. Here is a quote from its project page (bold markup added here):


  Back up and restore your Drupal MySQL database, code, and files or migrate a site between environments. Backup and Migrate supports gzip, bzip and zip compression as well as automatic scheduled backups.
  
  With Backup and Migrate you can dump some or all of your database tables to a file download or save to a file on the server or offsite, and to restore from an uploaded or previously saved database dump. You can choose which tables and what data to backup and cache data is excluded by default.


And there is even more: if your local environment (e.g. Win or Mac) differs from the OS that the server of your hosted website is running (like Linux), then these differences between OS-es imply potential extra challenges. I've had good experiences with the Backup and Migrate module between different OSes, which didn't cause any problems (worked fine) in situations where the typical MySql export / import failed before.