Adding some initial, plain text (no HTML <p> tag wraps the text) and e.g., bolding the last word, pressing enter after it removes a white space.

The easiest workaround is changing the NewLineMode property to Br.
Example:

   <telerik:RadEditor runat="server" ID="RadEditor1" NewLineMode="Br">
   </telerik:RadEditor>


More complex solution that will enable you continue using the paragraphs as new lines is by incorporating the following JavaScript code:

   <telerik:RadEditor runat="server" ID="RadEditor1">
   </telerik:RadEditor>

   <script type="text/javascript">
       Telerik.Web.UI.Editor.Utils.trimWhitespaceTextNodes = function () {

       };
   </script>

Note that the script should be put right after the RadEditor declaration to ensure that the RadEditor scripts are loaded.