This solution is applicable for editions Professional and below:
Salesforce is not designed to show you accounts that do not have opportunities associated to them.
A suggested alternative is to:
1. Run a report on all your opportunities. You will only need to display the Account Name and Account Site fields. Export this report to Excel.
2. Add a new column called "Opportunities" and add the value "Yes" in each row.
3. Add a new custom text field on the Accounts tab called "Opportunities."
4. Import the file to the accounts tab and update the accounts with this new field (ensure you select the 'overwrite existing account values' check box in step 5 of the import wizard).
5. You can then run a report on all accounts without opportunities.
6. In the last step of the report wizard in the 'Advanced filters' section, enter:
Opportunities | equals | <blank>.
You will have a list of all accounts without opportunities associated with them.
Note: For Enterprise edition and above, you can use the cross-filter functionality, using the filter Accounts Without Opportunities
For further information about cross filters, please refer to the articles:
Create a Cross Filter
Tips for Working with Cross Filters
To check the edition your organization is in, please go to: Setup > Administration Setup > Company Profile > Company Information and check the "Organization Edition" field