For most, Windows 7 Home Premium will be enough with a nice media and simple networking. This is probably the best choice for a computer that stays at home.

Windows Search has significantly improved over previous versions of Windows.

Home Group makes it easy to share and stream media, documents and printers over your home network.

Multi-Touch supported and improved handwriting recognition.

Media Center improvements with more formats supported.

For those who need it, Windows 7 Professional offers more advanced networking options as well as an option to run in XP mode for maximum compatibility.

Windows XP Mode improves compatibility with Windows XP programs

Encrypting File System protects data with advanced network backup

Location Aware Printing chooses printer preferences depending on where you are located.

Remote Desktop Host

Windows 7 Ultimate offers the same features that lesser editions do, but offers a few extra features. If you're worried about being mugged when transfering data between work and home, this may be the right choice.

BitLockerprotects data on removable devices like flash drives and external hard drives.

DirectAccess Use corporate resources on the road without a Virtual Private Network (VPN).

BranchCache Open files faster from another location

AppLocker Restricts unauthorized software and enables greater security.

MUI Switch between multiple languages quickly

Boot from VHD disk image