By default, each page you create (using the standard templates) seem to have Allow Attachments enabled. This may not necessarily be what you want because it means your visitors can also see the list of attachments to each specific page (e.g. file, images).
I personally prefer not to have the Allow Attachments enabled.
You can change this page by page. Or you can set up a template that you can choose when creating a page that has by default, Allow Attachments disabled.
Go to the page > More Actions > Page Settings > [uncheck] Allow Attachments
More Actions > Manage Site > Page Templates > Create Page Template > Select the kind of default template you want to modify (e.g. Web Page)
Give your new template a name (e.g. Web Page - No Attachment) > Create Template > (you will now be in edit mode of your new template) > Save
More Actions > Template Settings >
Here you can give a brief description of the template you created. This description will appear in the list of Page Templates and will help you remember what the template is about.
There are a number of other settings you can check/uncheck - all quite self-explanatory.
[uncheck] Allow Attachments
You can also set this as your default template is you like so you don't have to keep selecting it each time you create a new page.
[click] View Template Settings > [select your new template] > Set as default