I am using SharePoint 2007 and I want to approve users that have sent a request to access the SharePoint site.
How do I see who is requesting access so I can approve them?
There isn't a way to do this in Sharepoint 2007 like there is in Sharepoint 2013. You're out of luck unless you remove the option to request access and create some sort of request process where users ask for permission and then you add them manually or programmatically.
In SharePoint 2007 you dont have this option other than the email you received when customer request the access. If you want you can change the email address which can access the SharePoint access request.
Site Actions > Site Settings > Advanced Permissions (under "Users and Permissions" group ) > Settings > Access Requests
But in my opinion, it is really bad idea to handle the user request this way, because their is no track of it. Also when a site admin who is responsible for the request management left the company and you forget to change the access requests email then a big problem.
As an alternative, i think should create some kind of Infopath request farm to handle these requests.