Hi Cameron,
The Close Date field for Opportunities is required on both the table and screen levels, so you would have to modify both of those. Before doing this, please be aware that this could have implications on other parts of your account, for example if you had reports or workflows that assumed that all opportunities have a close date.
With that being said, here is how you could accomplish this. First, go to Customize > Tables / Fields and edit the Opportunities table. Scroll down to the CloseDate field, and uncheck the checkbox under the Required? column. Then click Finish Editing Fields.
Now that the field is not required on the table level, you can change the validations on the screens to not check for this field. The New Opportunity & Edit Opportunity screens have this validation and both work the same way. On the Save button actions, there is a conditional warning that checks for a blank value in the Close Date field:
You can remove these Conditional Warnings since the close date isn't required anymore.
Just let me know if you have any questions about this. If you'd like some help with this customization you could sign up for a consulting session: http://www.method.me/support/assisted-services/. To explore this possibility, please speak with your account rep.
Regards,
Russell