Try using single quotes...
<li><asp:HyperLink runat="server"
ID="lnkEmail"
ImageUrl="~/Images/emailicon.png"
NavigateUrl='mailto: <%# Eval("emailaddress") %>'></asp:HyperLink></li>
<li><asp:HyperLink runat="server"
ID="lnkWeb"
ImageUrl="~/Images/webicon.png"
NavigateUrl='<%# Eval("webaddress") %>'></asp:HyperLink></li>