I pre-ordered 3 copies of Home Premium this summer when it was on sale for $49.99 each. I've installed Windows 7 on my main PC and my netbook. I'll eventually install it on my Media computer as well. I didn't use Windows Vista much, so it will take some getting used to, but in my opinion, Windows 7 is the best version of Windows yet!
What has changed? For starters, it handles system resources extremely well compared to Windows Vista or XP. The user interface is very similar to Windows Vista, but they've added some nice features such as Aero Peek, Jump Lists, Snap, and thumbnail previews of windows on the taskbar, UAC is less annoying than Vista, Netflix is integrated into Media Center. Another nice feature is the ability to change the background of the logon screen (Which thanks to Tweaks.com Logon Changer for Windows 7, is extremely easy to do). One thing I don't like is that they removed the Sidebar that Windows Vista had, but it does still have Desktop Gadgets.
Should you upgrade? Well that depends on your situation. If you already have Windows Vista, and everything is working well for you, then it is probably not worth the expensive price tag (unless you qualify for a student copy or the free upgrade). In my opinion, there aren't $129 worth of new features added to Windows 7 from Vista, however it does run a lot better than Vista on most computers. If you are running XP on a newer machine, upgrading might not be a bad idea if your willing to pay the price. Also note that you cannot upgrade from Windows XP to Windows 7 without formatting your drive and doing a clean install (which erases everything).
Which edition is right for you? Windows 7 editions - Wikipedia helps answer that question. If you do not understand that, then Home Premium is probably good enough for you, unless you need to connect to a Domain at work (which requires Professional). Note that similar to Windows Vista, you can purchase edition upgrades without re-installing windows. Also note that Professional includes XP Mode, which gives you a virtual copy of Windows XP for compatibility. XP Mode is not worth paying extra money. If you still have a valid copy of XP, download VMware Player 3.0 for free with any edition and use it to create a Virutal Machine with Windows XP.
If you want to upgrade 3 computers to home premium, go for the family pack which gives you 3 licenses for $149.99 instead of $129.99 each. If you are a student, you can get a copy for $29.99.
Before you upgrade, you will want to make sure that all your hardware is compatible and has drivers for Windows 7. If you use any specialized software, check with the manufacturer to ensure it is compatible with Windows 7. If you are going to do a clean install (which I always recommend for best performance), then make sure you backup all your data and have the installers for all the software you need.