Or if by compatibility mode, you mean the ability to right click on a game and select a compatibility mode to run a game in, then yes it does. You right click on a game executable, select Troubleshoot Compatibility and follow the prompts. It's helped me play quite a few older games on both Windows 7 and Windows 8.
As Jenny and mj2c say, XP Mode (which involves downloading and installing XP using virtualization software such as Windows Virtual PC) is only available in Windows 7 Pro. However, it does not support 3D and is not suitable for gaming. It is intended to run legacy software in business environments. XP Mode in Windows 7 Pro will also no longer be supported by Microsoft after April 7th.
Gardening is better than therapy. Plus you get tomatoes.