Samsung Galaxy Nexus phone and Samsung Galaxy Nexus 7 tablet, as good as probably all other devices with Android 4.0 or higher on-board, are missing USB Mass Storage mode, which allowed you (under older Android) to use your mobile device as external hard drive and copy files directly via Windows Explorer.
Here you'll find some alternatives to transfer files from Android 4.0-based device.
If you're using Windows Vista, Windows 7 or newer, your system should have build-in MTP (Media Transfer Protocol). You can use it to easy transfer files, again using Windows Explorer. But this time, your device will not be mounted under any drive letter, so you can't access it using any regular application, that does not supports MTP.
If you're using Windows XP, you have to install Windows Media Player 10 or 11 or newer. Version 8 or 9 that comes with this system, has only partial support for MTP and you'll be only albe to transfer files TO your phone, and only store them in a folder one level under root folder. In most situations this is not enough, but installing newest version of WMP should fix these problems. Take a careful look at your hardware and minimum requirements for selected version of WMP. Version 10 should be enough and has by far less requirements than version 11 or 12.
Note, that after installing Windows Medial Player 10 or higher, you'll be able to access your files also through Windows Explorer (but as "mobile device", not a regular mounted disk drive -- see above). While with WMP 8 or 9 you can access it only inside player, with above restrictions.
For Windows 2000, you'll need Media Transfer Protocol Porting Kit from Microsoft.
This article is based on this blog post. Visit it to get information on transferring files to Mac or over WiFi.