Folks,
I had this problem with my PC (windows 7, 64-bit) and my iPad. After messing with it for a long time, I finally found the answer (bad USB driver). The following two step process should help resolve these kinds of problems more quickly.
The first step is to verify that the iPad (or iPhone) is really connected to your computer. This can be (really) checked using a program called USBDeview. You can get this (very small) program from http://download.cnet.com/USBDeview/3000-2094_4-10614190.html or http://www.nirsoft.net/utils/usb_devices_view.html. Don't worry, it's not Spyware or Malware.
Just run the program and sort on the 'Connected' column. If your iPad or iPhone doesn't show up as Yes (under 'Connected') then your iDevice is not properly connected to your computer. Could be a cable problem. Could be an iDevice problem. Could be a USB hub problem. Note that your iDevice might be listed as what it is (iPad or iPhone) or it might be listed as 'Apple Mobile Device USB Driver' in the 'Description' column.
Apple has a number of ideas to resolve this sort of basic connectivity issue, including switching USB ports, resetting your iDevice, rebooting your iDevice, rebooting your computer, etc. You will need to try them until your iDevice shows up in USBDeview as 'Yes' under Connected.
If you iDevice shows up as 'Yes' under connected, it should also be visible in the Device Manager (found in the Windows 7 Control Panel under Hardware and Sound). You might find it under Portable Devices or it might be under Universal Serial Bus controllers.
The iDevice may or may not show up in the Windows Explorer. On some machines it does, on others it does not. Why is not clear.
If the Idevice is properly known to Windows and iTunes can't see it, then any number of other things could be wrong. Apple has a list. See the very useful page over at http://support.apple.com/kb/TS1538. Testing shows that the Apple Mobile Device service must be running. Check this using Task Manager (started by right clicking the taskbar). Note that the iPod service and the iphlpsvc service must also be running. These services have different names under the Processes table versus the Services tab of Task Manager.
AppleMobileDeviceService.exe - Apple Mobile Device
iPodService.exe - iPod Service
ItunesHelper.exe - iphlpsvc
Step 4 of http://support.apple.com/kb/TS1538 checks if the Apple Mobile Device USB is installed. This is essential and a common source of problems. In at least some cases, Windows will install the 'MTP USB' driver. Indeed, Windows will reinstall this driver if you uninstall it. The MTP USB driver is essentially a Windows bug (possibly caused by Microsoft). You MUST replace the MTP USB driver with the Apple Mobile Device USB Driver. Step 4 explains how to do this. Note that you MUST use the 'Have Disk' approach. Otherwise, Windows will just reinstall the invalid MTP driver.
The Apple doc indicates that you can find the correct driver at C:\Program Files (x86)\Common Files\Apple\Mobile Device Support\Drivers. Perhaps this is correct on some systems. You may find the correct driver in C:\Program Files\Common Files\Apple\Mobile Device Support\Drivers.
iTunes could make this a lot easier by checking if the iDevice is known to Windows (what USBDevier does) and if the Apple Mobile Device USB driver is properly installed for the iDevice. Sadly it doesn't perform either check. Note that iTunes does if some of the related services (see above) are actually running.
