Check if System > Configuration > Advanced > Mage_Log is enabled.
Check if log observers are disabled in you local.xml or in some external module.
Below are the xml configuration to check if are enabled:
<frontend>
<events>
<controller_action_predispatch>
<observers><log><type>enabled</type></log></observers>
</controller_action_predispatch>
<controller_action_postdispatch>
<observers><log><type>enabled</type></log></observers>
</controller_action_postdispatch>
<customer_login>
<observers><log><type>enabled</type></log></observers>
</customer_login>
<customer_logout>
<observers><log><type>enabled</type></log></observers>
</customer_logout>
<sales_quote_save_after>
<observers><log><type>enabled</type></log></observers>
</sales_quote_save_after>
<checkout_quote_destroy>
<observers><log><type>enabled</type></log></observers>
</checkout_quote_destroy>
</events>
</frontend>