RX Lib (or RX Library) is large library of components and functions for Delphi all versions. New home of this library is on mirror site  and contains a full patch by Polaris group.
TRxRichEdit uses the RichEdit dll version 2 and therefore adds some functionality on top of the standard VCL TRichEdit. One of these functions is hyperlinks.
Drop a TRxLib component on a form, add an OnCreate event to the form with the following code:
procedure TForm1.FormCreate(Sender: TObject); var Attribs: TRxTextAttributes; begin RichEdit1.Text := 'This text has a link in it. And this is another link.'; RichEdit1.SelStart := 16; RichEdit1.SelLength := 4; Attribs := RichEdit1.WordAttributes; Attribs.Link := True; Attribs.Color := clBlue; RichEdit1.SelStart := 40; RichEdit1.SelLength := 12; Attribs := RichEdit1.WordAttributes; Attribs.Link := True; Attribs.Color := clBlue; RichEdit1.SelStart := 0; RichEdit1.SelLength := 0; end;
Add a URLClick event handler to the TRxRichEdit and implement it like this:
procedure TForm3.RxRichEdit1URLClick(Sender: TObject; const URLText: string; Button: TMouseButton); begin MessageDlg('You clicked on "' + URLText + '"', mtWarning, [mbOK], 0); end;
Now compile and run your program. You get a form containing the text with two links.
If you click on any of the links, you get a message telling you which link you clicked on.
Note: The TJvRichText control from the Jedi VCL also has this function since it is originally based on TRxRichEdit.