The Professional and Ultimate editions allow you to run software designed for Windows XP in XP Mode. This is basically a virtual machine running Windows XP and there are alternatives to Microsoft Virtual PC that you can use instead, such as VirtualBox. The only difference is that you'll need an XP installation CD to install XP into VirtualBox.
Another feature in Professional and Ultimate, but not Home Premium, is the ability to join a domain on a network. A large company with many networked PCs will split up the computers into small groups called domains. It's a handy feature, but home users won't ever use it and won't miss it if it's not there.
The Professional and Ultimate editions allow you to back up to a network, but it's another feature that few home users are interested in. It's much easier to plug in a USB drive and back up your files to it than to fiddle around with network servers. Besides, there are dozens of backup tools, some of which are free, that can back up to any device or network location.
BitLocker is only available in the Ultimate edition and it encrypts the contents of the disk to prevent thieves from stealing the data that is on it. It's useful for everyone, but it is not the only option for preventing data theft and Home Premium and Professional users could employ third party tools, some of which are free.
Finally, the Ultimate edition enables you to easily switch between 35 different languages. Do you really need to do this?
The obvious choice for most people is Windows 7 Home Premium. It has all the features you need and those that are missing are easily added using free software you can download from the internet in a few minutes.