You can use JVCL JvDocking components to drag and dock, in almost any version of Delphi. It's free and open source. The style with pins and close buttons is available using a docking style called the VID (visual interdev) style, that comes with JvDocking.

There are already a bunch of commercial alternatives also, and there is some support built into Delphi, which I find insufficient for my needs. While the Delphi IDE has its own internal docking library, tab support is very limited, slow, and in my subjective opinion, broken.
However, even on ancient delphi versions, Delphi 7 and up, JvDocking, provides all the functionality that the VCL's docking provides, plus more, so there's no problem ignoring the built in VCL functionality, which is to docking as TStringGrid is to real Grids.
Steps with JvDocking:
- Drop dock server and dock style object on main (host form) and connect them.
- Drop dock client component on the client (form to be docked) and connect it to the dockstyle.
- Configure properties of dock server.
- Run app. Have it create a form. Now drag the client form to an area that is made dockable by the dock server. Watch it dock nicely.
For docking in code demos see the JvDocking demos in the JVCL Examples folder.
Update
Or you can use what is built into the Delphi VCL since XE and XE2. XE and XE2 include a docking demo project named dockex.dpr
.
On Win7/Vista the demo is located at:
C:\Users\Public\Documents\RAD Studio\9.0\Samples\Delphi\VCL\Docking
Look here for the demo on Win XP:
C:\Documents and Settings\All Users\Documents\RAD Studio\9.0\Samples\Delphi\VCL\Docking
You should also check out the documentation for TDockTabSet
in the VCL, and the EDN article linked in the comments, which has source code you can download here. In my humble opinion, the Jedi JvDocking stuff is more professional and slick than the Docking Demo that ships with Delphi, but the built in stuff has the advantage of working without installing anything additional. I just tried the DockTabSet demo and the built in docking demos, and they are slow, and the painting is ugly and flickers. JvDocking looks professional. It's your call.