Any application and any peripheral which worked with Windows Vista should work with Windows 7 as Microsoft strove to prevent another compatibility disaster like the one associated with Windows Vista. In addition, some applications and devices which did not work with Windows Vista may work with Windows 7 due to expanded compatibility.
Aside from that, keep in mind that some software that fails to install or run on Windows 7 can be dealt with in one of three ways:
1.) Make sure you check back to the author's website for updated versions, patches, and drivers that enable Windows 7 compatibility. Not all software will be made compatible, but in the months after Windows 7's release you should see a dramatic increase in support by third-party vendors. Microsoft also offers a partital compatibility list for pre-purchase consultation.
2.) Use Compatibility Mode. Windows 7 is designed to enter Compatibility Mode automatically for programs it detects are designed for a previous version of Windows, but, like in Windows XP and Vista, it can be enabled manually. To manually enable Compatibility Mode, right-click the program, select Properties, and select the Compatibility tab. You can then enable Compatibility Mode for that program and select a previous version of Windows from the drop-down menu, among other options.
3.) Use XP Mode. Available to users of Windows 7 Professional and Ultimate editions, XP Mode is a feature that lets you install and run software in a downloadable Windows XP virtual machine. It enables you to continue to use older applications within Windows XP without resorting to purchasing an XP license and dual-booting XP along side Windows 7. Note, however, that XP Mode requires CPU support and increases RAM requirements, so it may not be an option for all users.
If you have a specific question about hardware or software compatibility feel free to start a new thread, but please check the above lists first.