The common controls include both comctl32.dll and riched20.dll. This page contains information about both of them. For a list of to-dos related to these DLLs, see DLLTodoList.
The MS Control Spy test application is another great way to look for problems: Bug 239: Test Wine with the Common Control Spy Samples
There is also a separate page with more details about HeaderControl.
Rebar is a layout control in comctl32.dll, but it's big and hairy.
The MS Control Spy test application can also ferret out rebar-specific bugs: Bug 239 Control Spy tool: Rebar.exe
Richedit is in its own dll, but is considered part of the common controls. While the info on his userpage may be out of date, MatthewFinnicum is a good person to ask about what remains to be done.
If need be, native riched20 can also be installed with winetricks.