Removing yourself from Visual Studio Team Services Accounts

This feature is now available in VSTS (now Azure DevOps Services). Login to one of your VSTS Account go to "My Profile". (top right corner) Then you can leave VSTS Accounts where your Account is a member.

Azure DevOps Services - leaving your organization

No, only account owner or administrator (in Project Collection Administrators group, Admin page > Security > Project Collection Administrators) can add or delete the account.