Had you run a upgrade before?  Check both connection string on your web.config file.  Check the Maschine Key with the Maschine Key of your old web.config

Could be an permission issue on your dnn folders and files, please check.

Try a restart of the application or the IIS.

Thanks for the input. I stumbled upon the solution late last night -- I was trying to create a user ID with a password of less than 7 characters. The web.config file specifies that passwords need to be at least 7 characters long. I thought about changing web.config, but I was still bothered that there was no feedback as to what the problem with the registration was. I stumbled upon another post from my home computer, but can't find it now, where others had experienced the same thing after upgrading to DNN 6.1, and somebody posted a few lines to add to the user.ascx file in the DesktopModules\Admin\Security folder. Since I can't find the post, I'll repost the lines that he suggested below. Now when I try to create a user with a password of less than 7 characters, it gives a warning. The registration works fine if the password length is satisfied.

 <asp:RequiredFieldValidator ID="passwordRequired" runat="server" CssClass="dnnFormMessage dnnFormError" ControlToValidate="txtPassword" ErrorMessage="Password is required" Display="Dynamic" />

<asp:RegularExpressionValidator ID="passwordLength" runat="server" CssClass="dnnFormMessage dnnFormError"  ControlToValidate="txtPassword" ErrorMessage="Minimum password length is 7" ValidationExpression=".{7}.*" Display="Dynamic" />

<asp:RequiredFieldValidator ID="confirmPasswordRequired" runat="server" CssClass="dnnFormMessage dnnFormError" ControlToValidate="txtConfirm" ErrorMessage="Password is required" Display="Dynamic" />